info
Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
"Without loss of generality" may not be formalizable
292 views
Skip to first unread message
Dan Christensen
Nov 21, 2022, 3:12:04 PM11/21/22
to
What is meant by "without loss of generality" in a mathematical proof?
"In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
"Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
--George Bergman
https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
Here I formally prove the following theorem from Wikipedia:
"If three objects are each painted either red or blue, then there must be at least two objects of the same color."
Wikipeda provides the following INFORMAL proof:
"A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
Formally, I prove (link below):
EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
Where
s = a set of 3 distinct elements: {x, y, z}
colors = a set of 2 distinct elements: {red, blue}
color(n) = the color of object n
I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
It seems unlikely that the without-loss-of-generality claim can be justified using the ordinary rules of logic found in most math textbooks as has been used here:
https://www.dcproof.com/WithoutLossOfGenerality.htm (new version)
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
"In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
"Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
--George Bergman
https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
Here I formally prove the following theorem from Wikipedia:
"If three objects are each painted either red or blue, then there must be at least two objects of the same color."
Wikipeda provides the following INFORMAL proof:
"A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
Formally, I prove (link below):
EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
Where
s = a set of 3 distinct elements: {x, y, z}
colors = a set of 2 distinct elements: {red, blue}
color(n) = the color of object n
I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
It seems unlikely that the without-loss-of-generality claim can be justified using the ordinary rules of logic found in most math textbooks as has been used here:
https://www.dcproof.com/WithoutLossOfGenerality.htm (new version)
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Blake Armanni
Nov 21, 2022, 3:45:50 PM11/21/22
to
Dan Christensen wrote:
> What is meant by "without loss of generality" in a mathematical proof?
you stupid nazi bitch. Here you have it, *_1.5_millions* Jews killed by
> What is meant by "without loss of generality" in a mathematical proof?
the khakhole khazar nazi "uKraine", expressed by a Jewish rabbi
F.U. Zelensky!
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/DV18sM4DEGY7
admitting *state_terrorism* on national tv, radio and massmedia. No shame.
Nord Stream (Sen. Ron Johnson, Victoria Nuland and Joe Biden)
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/K95EyXpmDd2E
Polish Man Tells Zelensky What He Thinks About His Falseflag
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/ZJN9FfuNhLXU
Dan Christensen
Nov 21, 2022, 3:55:04 PM11/21/22
to
On Monday, November 21, 2022 at 3:45:50 PM UTC-5, Blake Armanni wrote:
> Dan Christensen wrote:
>
> > What is meant by "without loss of generality" in a mathematical proof?
> you stupid ...
> Dan Christensen wrote:
>
> > What is meant by "without loss of generality" in a mathematical proof?
Hey, Nazi Boy, it seems your Red Army ain't what it used to be!
XAXAXA
Blake Armanni
Nov 21, 2022, 4:04:18 PM11/21/22
to
US Mercenaries Lost in Ukraine
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/gLEmoCMFe2X6/
here you have it, *_1.5_millions_* Jews killed by the khakhole khazar nazi
"uKraine", expressed by a truthful Jewish rabbi
Mike Terry
Nov 21, 2022, 4:23:29 PM11/21/22
to
On 21/11/2022 20:11, Dan Christensen wrote:
> What is meant by "without loss of generality" in a mathematical proof?
>
> "In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
>
> "Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
> --George Bergman
> https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
>
> Here I formally prove the following theorem from Wikipedia:
>
> "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
>
> Wikipeda provides the following INFORMAL proof:
>
> "A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
>
> https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
>
> Formally, I prove (link below):
>
> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
>
> Where
>
> s = a set of 3 distinct elements: {x, y, z}
>
> colors = a set of 2 distinct elements: {red, blue}
>
> color(n) = the color of object n
>
> I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
I would have thought the two sub-proofs should be /obviously/ alike - there's a symmetry in the
> What is meant by "without loss of generality" in a mathematical proof?
>
> "In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
>
> "Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
> --George Bergman
> https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
>
> Here I formally prove the following theorem from Wikipedia:
>
> "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
>
> Wikipeda provides the following INFORMAL proof:
>
> "A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
>
> https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
>
> Formally, I prove (link below):
>
> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
>
> Where
>
> s = a set of 3 distinct elements: {x, y, z}
>
> colors = a set of 2 distinct elements: {red, blue}
>
> color(n) = the color of object n
>
> I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
problem between red <--> blue.
>
> It seems unlikely that the without-loss-of-generality claim can be justified using the ordinary rules of logic [...]
WLOG is a kind of meta-proving strategy that cuts down the size of a proof so that it is clearer, or
more easily followed by the reader. E.g. it might exploit some symmetry in the problem to save the
reader from ploughing through many scenarios with essentially similar logic. Or it might identify a
superficially simpler scenario to deal with, with it being clear to the reader that proof of the
simpler scenario would readily enable proof of the full claim of the theorem.
It's expected that the reader will understand how the shortened proof would be expanded to a full
(more formal) proof, so the WLOG usage /could/ be completely avoided if required. That's why I
described it as a "meta-proving" strategy.
The logical justification behind the usage is that it is indeed seen by the reader that the longer
proof (without using WLOG) works. However, encapsulating precisely /why/ it works in one single
justification seems implausible. Within a formal proof system, the proof could just follow the
expanded proof without mentioning WLOG. (Hopefully you weren't suggesting there was anything
"fishy" about proofs phrased using WLOG.)
Regards,
Mike.
Dan Christensen
Nov 21, 2022, 4:31:23 PM11/21/22
to
Ross A. Finlayson
Nov 21, 2022, 5:22:23 PM11/21/22
to
And loosely defined, ....
Naifs.
Message has been deleted
Earle Jones
Nov 21, 2022, 8:00:47 PM11/21/22
to
Without loss of generality:
A Rhumba is a Navel movement without loss of semen.
earle
*
Dan Christensen
Nov 21, 2022, 8:06:45 PM11/21/22
to
STUDENTS BEWARE: Don't be a victim of AP's fake math and science
On Monday, November 21, 2022 at 5:37:02 PM UTC-5, Archimedes Plutonium wrote:
> >Dan Christensen ...
STUDENTS BEWARE: Don't be a victim of AP's fake math and science
[snip]
Time for another spanking, Archie Poo? When will you learn? Once again...
From his antics here at sci.math, it is obvious that AP has abandoned all hope being recognized as a credible personality. He is a malicious internet troll who now wants only to mislead and confuse students. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives. Is it revenge for his endless string of personal failures in life? Who knows.
In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
“0/0 must be equal to 1.”
-- June 9, 2015
“0 is an infinite irrational number.”
--June 28, 2015
“No negative numbers exist.”
--December 22, 2018
“Rationals are not numbers.”
--May 18, 2019
According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019
Which could explain...
“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019
AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:
“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019
AP seeks aid of Russian agents to promote failure in schools:
"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--November 9, 2017
And if that wasn't weird enough...
“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994
“The Universe itself is one gigantic big atom.”
--November 14, 2019
AP's sinister Atom God Cult of Failure???
“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)
On Monday, November 21, 2022 at 5:37:02 PM UTC-5, Archimedes Plutonium wrote:
> >Dan Christensen ...
STUDENTS BEWARE: Don't be a victim of AP's fake math and science
[snip]
Time for another spanking, Archie Poo? When will you learn? Once again...
From his antics here at sci.math, it is obvious that AP has abandoned all hope being recognized as a credible personality. He is a malicious internet troll who now wants only to mislead and confuse students. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives. Is it revenge for his endless string of personal failures in life? Who knows.
In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
“0/0 must be equal to 1.”
-- June 9, 2015
“0 is an infinite irrational number.”
--June 28, 2015
“No negative numbers exist.”
--December 22, 2018
“Rationals are not numbers.”
--May 18, 2019
According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019
Which could explain...
“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019
AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:
“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019
AP seeks aid of Russian agents to promote failure in schools:
"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--November 9, 2017
And if that wasn't weird enough...
“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994
“The Universe itself is one gigantic big atom.”
--November 14, 2019
AP's sinister Atom God Cult of Failure???
“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)
Archimedes Plutonium
Nov 21, 2022, 10:12:31 PM11/21/22
to
>Dan Christensen🤡 Math and Donna Strickland🃏 of Physics "Court Jester of Math"
On Friday, August 6, 2021 at 12:40:30 AM UTC-5, Michael Moroney (Kibo Parry M) wrote:
> fails at math and science:
Kibo Parry M. why is Dan Christensen a blithering idiot of logic with his 2 OR 1 = 3 with AND as subtraction???
Clearly he is insane in logic, but does he need a straightjacket??
Ruth Charney, Ken Ribet, Andrew Wiles, Terence Tao, Thomas Hales, John Stillwell, Jill Pipher, Ruth Charney, Ken Ribet, Andrew Beal, John Baez, Roger Penrose, Gerald Edgar, AMS, no-one there can do a Geometry Proof of Fundamental Theorem of Calculus, all they can offer is a limit analysis, so shoddy in logic they never realized that "analyzing" is not the same as "proving" for analyzing is much in the same as "measuring but not proving". And yet, none can do a geometry proof and the reason is quite clear for none can even see that the slant cut in single right-circular cone is a Oval, never the ellipse. So they could never do a geometry proof of FTC even if they wanted to. For they have no logical geometry brain to begin to do anything geometrical. Is it that Andrew Wiles and Terence Tao cannot understand the slant cut in single cone is an Oval, never the ellipse, or is it the foolish Boole logic they teach of 2 OR 1 = 3 with AND as subtraction? Not having a Logical brain to do math, for any rational person would be upset by Wiles, Tao saying truth table of AND is TFFF when it actually is TTTF. Is that why neither Terence Tao or Andrew Wiles can do a geometry proof Fundamental Theorem of Calculus?
Maybe they need to take up Earle Jones offer to wash dishes or pots at Stanford Univ or where ever, for they sure cannot do mathematics.
Why are these people failures of Math?? For none can even contemplate these 4 questions.
1) think a slant cut in single cone is a ellipse when it is proven to be a Oval, never the ellipse. For the cone and oval have 1 axis of symmetry, while ellipse has 2.
2) think Boole logic is correct with AND truth table being TFFF when it really is TTTF in order to avoid 2 OR 1 =3 with AND as subtraction
3) can never do a geometry proof of Fundamental Theorem of Calculus and are too ignorant in math to understand that analysis of something is not proving something in their "limit hornswaggle"
4) too stupid in science to ask the question of physics-- is the 1897 Thomson discovery of a 0.5MeV particle actually the Dirac magnetic monopole and that the muon is the true electron of atoms stuck inside a 840MeV proton torus doing the Faraday law. Showing that Peter Higgs, Sheldon Glashow, Ed Witten, John Baez, Roger Penrose, Arthur B. McDonald are sapheads when it comes to logical thinking in physics with their do nothing proton, do nothing electron.
Is Jim Holt, Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
John Venn, William Gustason, Richmond H. Thomason, more of propagandists and belong in "Abnormal Psychology" dept than in the department of logic, like Dan Christensen a laugh a minute logician? Probably because none can admit slant cut in single cone is a Oval, never the ellipse, due to axes of symmetry for cone and oval have 1 while ellipse has 2. Why they cannot even count beyond 1. Yet their minds were never good enough to see the error nor admit to their mistakes. They failed logic so badly they accept Boole's insane AND truth table of TFFF when it is TTTF avoiding the painful 2 OR 1 = 3 with AND as subtraction. Or is it because none of these logicians has a single marble of logic in their entire brain to realize calculus requires a geometry proof of Fundamental Theorem of Calculus, not a "limit analysis" for analysis is like a measurement, not a proving exercise. Analysis does not prove, only adds data and facts, but never is a proof of itself. I analyze things daily, and none of which is a proof. So are all these logicians like what Clutterfreak the propaganda stooge says they are.
> On Friday, July 2, 2021 at 9:47:42 AM UTC-5, Dan Christensen wrote:
> > You may be giving him too much credit here. Judging by his bizarre antics here, he has given up obtaining any kind of positive recognition.
> >
> > Dan
>
> Partial List of the World's Crackpot Logicians-- should be in a college Abnormal-Psychology department, not Logic//
>
> Peter Bruce Andrews, Lennart Aqvist, Henk Barendregt, John Lane Bell, Nuel Belnap,
> Paul Benacerraf, Jean Paul Van Bendegem, Johan van Benthem, Jean-Yves Beziau,
> Andrea Bonomi, Nicolas Bourbaki (a group of logic fumblers), Alan Richard Bundy, Gregory Chaitin,
> Jack Copeland, John Corcoran, Dirk van Dalen, Martin Davis, Michael A.E. Dummett, John Etchemendy, Hartry Field, Kit Fine, Melvin Fitting, Matthew Foreman, Michael Fourman,
> Harvey Friedman, Dov Gabbay, L.T.F. Gamut (group of logic fumblers), Sol Garfunkel, Jean-Yves Girard, Siegfried Gottwald, Jeroen Groenendijk, Susan Haack, Leo Harrington, William Alvin Howard,
> Ronald Jensen, Dick de Jongh, David Kaplan, Alexander S. Kechris, Howard Jerome Keisler,
> Robert Kowalski, Georg Kreisel, Saul Kripke, Kenneth Kunen, Karel Lambert, Penelope Maddy,
> David Makinson, Isaac Malitz, Gary R. Mar, Donald A. Martin, Per Martin-Lof,Yiannis N. Moschovakis, Jeff Paris, Charles Parsons, Solomon Passy, Lorenzo Pena, Dag Prawitz,
> Graham Priest, Michael O. Rabin, Gerald Sacks, Dana Scott, Stewart Shapiro, Theodore Slaman,
> Robert M. Solovay, John R. Steel, Martin Stokhof, Anne Sjerp Troelstra, Alasdair Urquhart,
> Moshe Y. Vardi, W. Hugh Woodin, John Woods
>
> Now I should include the authors of Logic textbooks for they, more than most, perpetuate and crank the error filled logic, the Horrible Error of 2 OR 1 = 3 with 2 AND 1 = 1, that is forced down the throats of young students, making them cripples of ever thinking straight and clearly.
>
> Many of these authors have passed away but their error filled books are a scourge to modern education
>
> George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap,
> Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi, Michael Withey,
> Patrick Hurley, Harry J Gensler, David Kelley, Jesse Bollinger, Theodore Sider,
> David Barker-Plummer, I. C. Robledo, John Nolt, Peter Smith, Stan Baronett, Jim Holt,
> Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
> John Venn, William Gustason, Richmond H. Thomason,
> > #5-1, 134th published book
> >
> > > > > Introduction to TEACHING TRUE MATHEMATICS: Volume 1 for ages 5 through 26, math textbook series, book 1 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > The 134th book of AP, and belatedly late, for I had already written the series of TEACHING TRUE MATHEMATICS in a 7 volume, 8 book set. This would be the first book in that 8 book set (one of the books is a companion book to 1st year college). But I suppose that I needed to write the full series before I could write the Introduction and know what I had to talk about and talk about in a logical progression order. Sounds paradoxical in a sense, that I needed to write the full series first and then go back and write the Introduction. But in another sense, hard to write an introduction on something you have not really fully done and completed. For example to know what is error filled Old Math and to list those errors in a logical order requires me to write the full 7 volumes in order to list in order the mistakes.
> >
> > Cover Picture: Mathematics begins with counting, with numbers, with quantity. But counting numbers needs geometry for something to count in the first place. So here in this picture of the generalized Hydrogen atom of chemistry and physics is a torus geometry of 8 rings of a proton torus and one ring where my fingers are, is a equator ring that is the muon and thrusting through the proton torus at the equator of the torus. So we count 9 rings in all. So math is created by atoms and math numbers exist because atoms have many geometry figures to count. And geometry exists because atoms have shapes and different figures.
> >
> > Product details
> > • ASIN : B08K2XQB4M
> > • Publication date : September 24, 2020
> > • Language : English
> > • File size : 576 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 23 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #224,974 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3 in 45-Minute Science & Math Short Reads
> > ◦ #23 in Calculus (Kindle Store)
> > ◦ #182 in Calculus (Books)
> >
> >
> >
> > #5-2, 45th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> >
> >
> >
> > #1 New Releasein General Geometry
> >
> >
> > Last revision was 2NOV2020. And this is AP's 45th published book of science.
> > Preface: Volume 2 takes the 5 year old student through to senior in High School for their math education.
> >
> > This is a textbook series in several volumes that carries every person through all his/her math education starting age 5 up to age 26. Volume 2 is for age 5 year old to that of senior in High School, that is needed to do both science and math. Every other math book is incidental to this series of Teaching True Mathematics.
> >
> > It is a journal-textbook because Amazon's Kindle offers me the ability to edit overnight, and to change the text, almost on a daily basis. A unique first in education textbooks-- almost a continual overnight editing. Adding new text, correcting text. Volume 2 takes the 5 year old student through to senior in High School for their math education. Volume 3 carries the Freshperson in College for their math calculus education.
> >
> > Cover Picture: The Numbers as Integers from 0 to 100, and 10 Grid when dividing by 10, and part of the 100 Grid when dividing by 100. Decimal Grid Numbers are the true numbers of mathematics. The Reals, the rationals & irrationals, the algebraic & transcendentals, the imaginary & Complex, and the negative-numbers are all fake numbers. For, to be a true number, you have to "be counted" by mathematical induction. The smallest Grid system is the Decimal 10 Grid.
> >
> > Length: 399 pages
> >
> >
> >
> >
> > Product details
> > ASIN : B07RG7BVZW
> > Publication date : May 2, 2019
> > Language : English
> > File size : 2023 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 399 pages
> > Lending : Enabled
> > Best Sellers Rank: #235,426 in Kindle Store (See Top 100 in Kindle Store)
> > #15 in General Geometry
> > #223 in Geometry & Topology (Books)
> >
> >
> >
> >
> > #5-3, 55th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 3 for age 18-19, 1st year College Calculus, math textbook series, book 3 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 25Jun2021. And this is AP's 55th published book of science.
> >
> > Teaching True Mathematics, by Archimedes Plutonium 2019
> >
> > Preface: This is volume 3, book 3 of Teaching True Mathematics, designed for College Freshperson students, 1st year college students of age 18-19. It is the continuation of volume 2 for ages 5 through 18 years old.
> >
> > The main major topic is the AP-EM equations of electricity and magnetism, the mathematics for the laws of electricity and magnetism; what used to be called the Maxwell Equations of Physics. The 1st Year College Math has to prepare all students with the math for all the sciences. So 1st year college Math is like a huge intersection station that has to prepare students with the math they need to do the hard sciences such as physics, chemistry, biology, astronomy, geology, etc. What this means is, 1st year college is calculus that allows the student to work with electricity and magnetism. All the math that is needed to enable students to do electricity and magnetism. In Old Math before this textbook, those Old Math textbooks would end in 1/3 of the text about Arclength, vector space, div, curl, Line Integral, Green's, Stokes, Divergence theorem trying to reach and be able to teach Maxwell Equations. But sadly, barely any Old Math classroom reached that 1/3 ending of the textbook, and left all those college students without any math to tackle electricity and magnetism. And most of Old Math was just muddle headed wrong even if they covered the last 1/3 of the textbook. And that is totally unacceptable in science. This textbook fixes that huge hole and gap in Old Math education.
> >
> > And there is no way around it, that a course in 1st year College Calculus is going to do a lot of hands on experiment with electricity and magnetism, and is required of the students to buy a list of physics apparatus-- multimeter, galvanometer, coil, bar magnet, alligator clip wires, electromagnet, iron filing case, and possibly even a 12 volt transformer, all shown in the cover picture. The beginning of this textbook and the middle section all leads into the ending of this textbook-- we learn the AP-EM Equations and how to use those equations. And there is no escaping the fact that it has to be hands on physics experiments in the classroom of mathematics.
> >
> > But, do not be scared, for this is all easy easy easy. For if you passed and enjoyed Volume 2 TEACHING TRUE MATHEMATICS, then I promise you, you will not be stressed with Volume 3, for I go out of my way to make it clear and understandable.
> >
> > Warning: this is a Journal Textbook, meaning that I am constantly adding new material, constantly revising, constantly fixing mistakes or making things more clear. So if you read this book in August of 2019, chances are it is different when you read it in September 2019. Ebooks allow authors the freedom to improve their textbooks on a ongoing basis.
> >
> > The 1st year college math should be about the math that prepares any and all students for science, whether they branch out into physics, chemistry, biology, geology, astronomy, or math, they should have all the math in 1st year college that will carry them through those science studies. I make every attempt possible to make math easy to understand, easy to learn and hopefully fun.
> >
> > Product details
> > • ASIN : B07WN9RVXD
> > • Publication date : August 16, 2019
> > • Language : English
> > • File size : 1390 KB
> > • Simultaneous device usage : Unlimited
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 236 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #1,377,070 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #411 in Calculus (Kindle Store)
> > ◦ #2,480 in Calculus (Books)
> >
> >
> >
> >
> > #5-4, 56th published book
> >
> > COLLEGE CALCULUS GUIDE to help students recognize math professor spam from math truth & reality// math textbook series, book 4 Kindle Edition
> >
> > by Archimedes Plutonium (Author)
> >
> >
> > #1 New Releasein 15-Minute Science & Math Short Reads
> >
> >
> > This textbook is the companion guide book to AP's Teaching True Mathematics, 1st year College. It is realized that Old Math will take a long time in removing their fake math, so in the interim period, this Guide book is designed to speed up the process of removing fake Calculus out of the education system, the fewer students we punish with forcing them with fake Calculus, the better we are.
> > Cover Picture: This book is part comedy, for when you cannot reason with math professors that they have many errors to fix, that 90% of their Calculus is in error, you end up resorting to comedy, making fun of them, to prod them to fix their errors. To prod them to "do right by the students of the world" not their entrenched propaganda.
> > Length: 54 pages
> >
> >
> > Product details
> > File Size: 1035 KB
> > Print Length: 64 pages
> > Simultaneous Device Usage: Unlimited
> > Publication Date: August 18, 2019
> > Sold by: Amazon.com Services LLC
> > Language: English
> > ASIN: B07WNGLQ85
> > Text-to-Speech: Enabled
> > X-Ray: Not Enabled
> > Word Wise: Not Enabled
> > Lending: Enabled
> > Enhanced Typesetting: Enabled
> > Amazon Best Sellers Rank: #253,425 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
> > #38 in 90-Minute Science & Math Short Reads
> > #318 in Calculus (Books)
> > #48 in Calculus (Kindle Store)
> >
> > #5-5, 72nd published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 4 for age 19-20 Sophomore-year College, math textbook series, book 5 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Preface: This is volume 4, book 5 of Teaching True Mathematics, designed for College Sophomore-year students, students of age 19-20. It is the continuation of volume 3 in the end-goal of learning how to do the mathematics of electricity and magnetism, because everything in physics is nothing but atoms and atoms are nothing but electricity and magnetism. To know math, you have to know physics. We learned the Calculus of 2nd dimension and applied it to the equations of physics for electricity and magnetism. But we did not learn the calculus of those equations for 3rd dimension. So, you can say that Sophomore year College math is devoted to 3D Calculus. This sophomore year college we fill in all the calculus, and we start over on all of Geometry, for geometry needs a modern day revision. And pardon me for this book is mostly reading, and the students doing less calculations. The classroom of this textbook has the teacher go through page by page to get the students comprehending and understanding of what is being taught. There are many hands on experiments also.
> >
> > Cover Picture shows some toruses, some round some square, torus of rings, thin strips of rings or squares and shows them laid flat. That is Calculus of 3rd dimension that lays a ring in a torus to be flat in 2nd dimension.
> > Length: 105 pages
> >
> > Product details
> > • ASIN : B0828M34VL
> > • Publication date : December 2, 2019
> > • Language : English
> > • File size : 952 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 105 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #242,037 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #36 in Calculus (Kindle Store)
> > ◦ #219 in Calculus (Books)
> >
> >
> > #5-6, 75th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 5 for age 20-21 Junior-year of College, math textbook series, book 6 Kindle Edition
> > by Archimedes Plutonium 2019
> >
> > This is volume 5, book 6 of Teaching True Mathematics, designed for College Junior-year students, students of age 20-21. In first year college Calculus we learned calculus of the 2nd dimension and applied it to the equations of physics for electricity and magnetism. And in sophomore year we learned calculus of 3rd dimension to complete our study of the mathematics needed to do the physics of electricity and magnetism. Now, junior year college, we move onto something different, for we focus mostly on logic now and especially the logic of what is called the "mathematical proof". Much of what the student has learned about mathematics so far has been given to her or him as stated knowledge, accept it as true because I say so. But now we are going to do math proofs. Oh, yes, we did prove a few items here and there, such as why the Decimal Grid Number system is so special, such as the Pythagorean Theorem, such as the Fundamental Theorem of Calculus with its right-triangle hinged up or down. But many ideas we did not prove, we just stated them and expected all students to believe them true. And you are now juniors in college and we are going to start to prove many of those ideas and teach you "what is a math proof". Personally, I myself feel that the math proof is overrated, over hyped. But the math proof is important for one reason-- it makes you better scientists of knowing what is true and what is a shaky idea. A math proof is the same as "thinking straight and thinking clearly". And all scientists need to think straight and think clearly. But before we get to the Mathematics Proof, we have to do Probability and Statistics. What you learned in Grade School, then High School, then College, called Sigma Error, now becomes Probability and Statistics. It is important because all sciences including mathematics needs and uses Probability and Statistics. So, our job for junior-year of college mathematics is all cut out and ahead for us, no time to waste, let us get going.
> >
> > Cover Picture: is a sample of the Array Proof, a proof the ellipse is not a conic but rather a cylinder cut wherein the oval is the slant cut of a cone, not the ellipse.
> >
> > Length: 175 pages
> >
> >
> > Product details
> > ASIN : B0836F1YF6
> > Publication date : December 26, 2019
> > Language : English
> > File size : 741 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 175 pages
> > Lending : Enabled
> > Best Sellers Rank: #3,768,255 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3,591 in Probability & Statistics (Kindle Store)
> > ◦ #19,091 in Probability & Statistics (Books)
> >
> >
> >
> > #5-7, 89th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 6 for age 21-22 Senior-year of College, math textbook series, book 7 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revision was 6Feb2021.
> > Preface: This is the last year of College for mathematics and we have to mostly summarize all of mathematics as best we can. And set a new pattern to prepare students going on to math graduate school. A new pattern of work habits, because graduate school is more of research and explore on your own. So in this final year, I am going to eliminate tests, and have it mostly done as homework assignments.
> >
> > Cover Picture: Again and again, many times in math, the mind is not good enough alone to think straight and clear, and you need tools to hands-on see how it works. Here is a collection of tools for this senior year college classes. There is a pencil, clipboard, graph paper, compass, divider, protractor, slide-ruler. And for this year we spend a lot of time on the parallelepiped, showing my wood model, and showing my erector set model held together by wire loops in the corners. The plastic square is there only to hold up the erector set model.
> >
> > Length: 110 pages
> >
> > Product details
> > ASIN : B084V11BGY
> > Publication date : February 15, 2020
> > Language : English
> > File size : 826 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Enabled
> > Print length : 110 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,965 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #345 in Mathematics (Kindle Store)
> > ◦ #373 in Physics (Kindle Store)
> > ◦ #2,256 in Physics (Books)
> >
> > #5-8, 90th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 7 for age 22-26 Graduate school, math textbook series, book 8 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revised 1NOV2020. This was AP's 90th published book of science.
> >
> > Preface: This is College Graduate School mathematics. Congratulations, you made it this far. To me, graduate school is mostly research, research mathematics and that means also physics. So it is going to be difficult to do math without physics. Of course, we focus on the mathematics of these research projects.
> >
> > My textbook for Graduate school is just a template and the professors teaching the graduate students are free of course to follow their own projects, but in terms of being physics and math combined. What I list below is a template for possible projects.
> >
> > So, in the below projects, I list 36 possible research projects that a graduate student my like to undertake, or partake. I list those 36 projects with a set of parentheses like this (1), (2), (3), etc. Not to be confused with the chapters listing as 1), 2), 3), etc. I list 36 projects but the professor can offer his/her own list, and I expect students with their professor, to pick a project and to monitor the student as to his/her progresses through the research. I have listed each project then cited some of my own research into these projects, below each project is an entry. Those entries are just a help or helper in getting started or acquainted with the project. The entry has a date time group and a newsgroup that I posted to such as sci.math or plutonium-atom-universe Google newsgroups. Again the entry is just a help or helper in getting started.
> >
> > Now instead of picking one or two projects for your Graduate years of study, some may select all 36 projects where you write a short paper on each project. Some may be bored with just one or two projects and opt for all 36.
> >
> > Cover Picture: A photo by my iphone of a page on Permutations of the Jacobs book Mathematics: A Human Endeavor, 1970. One of the best textbooks ever written in Old Math, not for its contents because there are many errors, but for its teaching style. It is extremely rare to find a math textbook written for the student to learn. Probably because math professors rarely learned how to teach in the first place; only learned how to unintentionally obfuscate. The page I photographed is important because it is the interface between geometry's perimeter or surface area versus geometry's area or volume, respectively. Or, an interface of pure numbers with that of geometry. But I have more to say on this below.
> > Length: 296 pages
> >
> > Product details
> > ASIN : B085DF8R7V
> > Publication date : March 1, 2020
> > Language : English
> > File size : 828 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 296 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,981 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #13 in General Geometry
> > ◦ #213 in Geometry & Topology (Books)
> >
> >
> >
> > #5-8, 160th published book
> >
> > MATHOPEDIA-- List of 80 fakes and mistakes of Old Math// Student teaches professor Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 28Apr2022. And this is AP's 160th book of Science.
> > Preface:
> > A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.
> > The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.
> > The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery. I know because I have been there.
> > Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.
> > I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).
> >
> > Product details
> > • ASIN : B09MZTLRL5
> > • Publication date : December 2, 2021
> > • Language : English
> > • File size : 1149 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 65 pages
> > • Lending : Enabled
On Friday, August 6, 2021 at 12:40:30 AM UTC-5, Michael Moroney (Kibo Parry M) wrote:
> fails at math and science:
Kibo Parry M. why is Dan Christensen a blithering idiot of logic with his 2 OR 1 = 3 with AND as subtraction???
Clearly he is insane in logic, but does he need a straightjacket??
Ruth Charney, Ken Ribet, Andrew Wiles, Terence Tao, Thomas Hales, John Stillwell, Jill Pipher, Ruth Charney, Ken Ribet, Andrew Beal, John Baez, Roger Penrose, Gerald Edgar, AMS, no-one there can do a Geometry Proof of Fundamental Theorem of Calculus, all they can offer is a limit analysis, so shoddy in logic they never realized that "analyzing" is not the same as "proving" for analyzing is much in the same as "measuring but not proving". And yet, none can do a geometry proof and the reason is quite clear for none can even see that the slant cut in single right-circular cone is a Oval, never the ellipse. So they could never do a geometry proof of FTC even if they wanted to. For they have no logical geometry brain to begin to do anything geometrical. Is it that Andrew Wiles and Terence Tao cannot understand the slant cut in single cone is an Oval, never the ellipse, or is it the foolish Boole logic they teach of 2 OR 1 = 3 with AND as subtraction? Not having a Logical brain to do math, for any rational person would be upset by Wiles, Tao saying truth table of AND is TFFF when it actually is TTTF. Is that why neither Terence Tao or Andrew Wiles can do a geometry proof Fundamental Theorem of Calculus?
Maybe they need to take up Earle Jones offer to wash dishes or pots at Stanford Univ or where ever, for they sure cannot do mathematics.
Why are these people failures of Math?? For none can even contemplate these 4 questions.
1) think a slant cut in single cone is a ellipse when it is proven to be a Oval, never the ellipse. For the cone and oval have 1 axis of symmetry, while ellipse has 2.
2) think Boole logic is correct with AND truth table being TFFF when it really is TTTF in order to avoid 2 OR 1 =3 with AND as subtraction
3) can never do a geometry proof of Fundamental Theorem of Calculus and are too ignorant in math to understand that analysis of something is not proving something in their "limit hornswaggle"
4) too stupid in science to ask the question of physics-- is the 1897 Thomson discovery of a 0.5MeV particle actually the Dirac magnetic monopole and that the muon is the true electron of atoms stuck inside a 840MeV proton torus doing the Faraday law. Showing that Peter Higgs, Sheldon Glashow, Ed Witten, John Baez, Roger Penrose, Arthur B. McDonald are sapheads when it comes to logical thinking in physics with their do nothing proton, do nothing electron.
Is Jim Holt, Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
John Venn, William Gustason, Richmond H. Thomason, more of propagandists and belong in "Abnormal Psychology" dept than in the department of logic, like Dan Christensen a laugh a minute logician? Probably because none can admit slant cut in single cone is a Oval, never the ellipse, due to axes of symmetry for cone and oval have 1 while ellipse has 2. Why they cannot even count beyond 1. Yet their minds were never good enough to see the error nor admit to their mistakes. They failed logic so badly they accept Boole's insane AND truth table of TFFF when it is TTTF avoiding the painful 2 OR 1 = 3 with AND as subtraction. Or is it because none of these logicians has a single marble of logic in their entire brain to realize calculus requires a geometry proof of Fundamental Theorem of Calculus, not a "limit analysis" for analysis is like a measurement, not a proving exercise. Analysis does not prove, only adds data and facts, but never is a proof of itself. I analyze things daily, and none of which is a proof. So are all these logicians like what Clutterfreak the propaganda stooge says they are.
> On Friday, July 2, 2021 at 9:47:42 AM UTC-5, Dan Christensen wrote:
> > You may be giving him too much credit here. Judging by his bizarre antics here, he has given up obtaining any kind of positive recognition.
> >
> > Dan
>
> Partial List of the World's Crackpot Logicians-- should be in a college Abnormal-Psychology department, not Logic//
>
> Peter Bruce Andrews, Lennart Aqvist, Henk Barendregt, John Lane Bell, Nuel Belnap,
> Paul Benacerraf, Jean Paul Van Bendegem, Johan van Benthem, Jean-Yves Beziau,
> Andrea Bonomi, Nicolas Bourbaki (a group of logic fumblers), Alan Richard Bundy, Gregory Chaitin,
> Jack Copeland, John Corcoran, Dirk van Dalen, Martin Davis, Michael A.E. Dummett, John Etchemendy, Hartry Field, Kit Fine, Melvin Fitting, Matthew Foreman, Michael Fourman,
> Harvey Friedman, Dov Gabbay, L.T.F. Gamut (group of logic fumblers), Sol Garfunkel, Jean-Yves Girard, Siegfried Gottwald, Jeroen Groenendijk, Susan Haack, Leo Harrington, William Alvin Howard,
> Ronald Jensen, Dick de Jongh, David Kaplan, Alexander S. Kechris, Howard Jerome Keisler,
> Robert Kowalski, Georg Kreisel, Saul Kripke, Kenneth Kunen, Karel Lambert, Penelope Maddy,
> David Makinson, Isaac Malitz, Gary R. Mar, Donald A. Martin, Per Martin-Lof,Yiannis N. Moschovakis, Jeff Paris, Charles Parsons, Solomon Passy, Lorenzo Pena, Dag Prawitz,
> Graham Priest, Michael O. Rabin, Gerald Sacks, Dana Scott, Stewart Shapiro, Theodore Slaman,
> Robert M. Solovay, John R. Steel, Martin Stokhof, Anne Sjerp Troelstra, Alasdair Urquhart,
> Moshe Y. Vardi, W. Hugh Woodin, John Woods
>
> Now I should include the authors of Logic textbooks for they, more than most, perpetuate and crank the error filled logic, the Horrible Error of 2 OR 1 = 3 with 2 AND 1 = 1, that is forced down the throats of young students, making them cripples of ever thinking straight and clearly.
>
> Many of these authors have passed away but their error filled books are a scourge to modern education
>
> George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap,
> Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi, Michael Withey,
> Patrick Hurley, Harry J Gensler, David Kelley, Jesse Bollinger, Theodore Sider,
> David Barker-Plummer, I. C. Robledo, John Nolt, Peter Smith, Stan Baronett, Jim Holt,
> Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
> John Venn, William Gustason, Richmond H. Thomason,
> > #5-1, 134th published book
> >
> > > > > Introduction to TEACHING TRUE MATHEMATICS: Volume 1 for ages 5 through 26, math textbook series, book 1 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > The 134th book of AP, and belatedly late, for I had already written the series of TEACHING TRUE MATHEMATICS in a 7 volume, 8 book set. This would be the first book in that 8 book set (one of the books is a companion book to 1st year college). But I suppose that I needed to write the full series before I could write the Introduction and know what I had to talk about and talk about in a logical progression order. Sounds paradoxical in a sense, that I needed to write the full series first and then go back and write the Introduction. But in another sense, hard to write an introduction on something you have not really fully done and completed. For example to know what is error filled Old Math and to list those errors in a logical order requires me to write the full 7 volumes in order to list in order the mistakes.
> >
> > Cover Picture: Mathematics begins with counting, with numbers, with quantity. But counting numbers needs geometry for something to count in the first place. So here in this picture of the generalized Hydrogen atom of chemistry and physics is a torus geometry of 8 rings of a proton torus and one ring where my fingers are, is a equator ring that is the muon and thrusting through the proton torus at the equator of the torus. So we count 9 rings in all. So math is created by atoms and math numbers exist because atoms have many geometry figures to count. And geometry exists because atoms have shapes and different figures.
> >
> > Product details
> > • ASIN : B08K2XQB4M
> > • Publication date : September 24, 2020
> > • Language : English
> > • File size : 576 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 23 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #224,974 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3 in 45-Minute Science & Math Short Reads
> > ◦ #23 in Calculus (Kindle Store)
> > ◦ #182 in Calculus (Books)
> >
> >
> >
> > #5-2, 45th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> >
> >
> >
> > #1 New Releasein General Geometry
> >
> >
> > Last revision was 2NOV2020. And this is AP's 45th published book of science.
> > Preface: Volume 2 takes the 5 year old student through to senior in High School for their math education.
> >
> > This is a textbook series in several volumes that carries every person through all his/her math education starting age 5 up to age 26. Volume 2 is for age 5 year old to that of senior in High School, that is needed to do both science and math. Every other math book is incidental to this series of Teaching True Mathematics.
> >
> > It is a journal-textbook because Amazon's Kindle offers me the ability to edit overnight, and to change the text, almost on a daily basis. A unique first in education textbooks-- almost a continual overnight editing. Adding new text, correcting text. Volume 2 takes the 5 year old student through to senior in High School for their math education. Volume 3 carries the Freshperson in College for their math calculus education.
> >
> > Cover Picture: The Numbers as Integers from 0 to 100, and 10 Grid when dividing by 10, and part of the 100 Grid when dividing by 100. Decimal Grid Numbers are the true numbers of mathematics. The Reals, the rationals & irrationals, the algebraic & transcendentals, the imaginary & Complex, and the negative-numbers are all fake numbers. For, to be a true number, you have to "be counted" by mathematical induction. The smallest Grid system is the Decimal 10 Grid.
> >
> > Length: 399 pages
> >
> >
> >
> >
> > Product details
> > ASIN : B07RG7BVZW
> > Publication date : May 2, 2019
> > Language : English
> > File size : 2023 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 399 pages
> > Lending : Enabled
> > Best Sellers Rank: #235,426 in Kindle Store (See Top 100 in Kindle Store)
> > #15 in General Geometry
> > #223 in Geometry & Topology (Books)
> >
> >
> >
> >
> > #5-3, 55th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 3 for age 18-19, 1st year College Calculus, math textbook series, book 3 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 25Jun2021. And this is AP's 55th published book of science.
> >
> > Teaching True Mathematics, by Archimedes Plutonium 2019
> >
> > Preface: This is volume 3, book 3 of Teaching True Mathematics, designed for College Freshperson students, 1st year college students of age 18-19. It is the continuation of volume 2 for ages 5 through 18 years old.
> >
> > The main major topic is the AP-EM equations of electricity and magnetism, the mathematics for the laws of electricity and magnetism; what used to be called the Maxwell Equations of Physics. The 1st Year College Math has to prepare all students with the math for all the sciences. So 1st year college Math is like a huge intersection station that has to prepare students with the math they need to do the hard sciences such as physics, chemistry, biology, astronomy, geology, etc. What this means is, 1st year college is calculus that allows the student to work with electricity and magnetism. All the math that is needed to enable students to do electricity and magnetism. In Old Math before this textbook, those Old Math textbooks would end in 1/3 of the text about Arclength, vector space, div, curl, Line Integral, Green's, Stokes, Divergence theorem trying to reach and be able to teach Maxwell Equations. But sadly, barely any Old Math classroom reached that 1/3 ending of the textbook, and left all those college students without any math to tackle electricity and magnetism. And most of Old Math was just muddle headed wrong even if they covered the last 1/3 of the textbook. And that is totally unacceptable in science. This textbook fixes that huge hole and gap in Old Math education.
> >
> > And there is no way around it, that a course in 1st year College Calculus is going to do a lot of hands on experiment with electricity and magnetism, and is required of the students to buy a list of physics apparatus-- multimeter, galvanometer, coil, bar magnet, alligator clip wires, electromagnet, iron filing case, and possibly even a 12 volt transformer, all shown in the cover picture. The beginning of this textbook and the middle section all leads into the ending of this textbook-- we learn the AP-EM Equations and how to use those equations. And there is no escaping the fact that it has to be hands on physics experiments in the classroom of mathematics.
> >
> > But, do not be scared, for this is all easy easy easy. For if you passed and enjoyed Volume 2 TEACHING TRUE MATHEMATICS, then I promise you, you will not be stressed with Volume 3, for I go out of my way to make it clear and understandable.
> >
> > Warning: this is a Journal Textbook, meaning that I am constantly adding new material, constantly revising, constantly fixing mistakes or making things more clear. So if you read this book in August of 2019, chances are it is different when you read it in September 2019. Ebooks allow authors the freedom to improve their textbooks on a ongoing basis.
> >
> > The 1st year college math should be about the math that prepares any and all students for science, whether they branch out into physics, chemistry, biology, geology, astronomy, or math, they should have all the math in 1st year college that will carry them through those science studies. I make every attempt possible to make math easy to understand, easy to learn and hopefully fun.
> >
> > Product details
> > • ASIN : B07WN9RVXD
> > • Publication date : August 16, 2019
> > • Language : English
> > • File size : 1390 KB
> > • Simultaneous device usage : Unlimited
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 236 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #1,377,070 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #411 in Calculus (Kindle Store)
> > ◦ #2,480 in Calculus (Books)
> >
> >
> >
> >
> > #5-4, 56th published book
> >
> > COLLEGE CALCULUS GUIDE to help students recognize math professor spam from math truth & reality// math textbook series, book 4 Kindle Edition
> >
> > by Archimedes Plutonium (Author)
> >
> >
> > #1 New Releasein 15-Minute Science & Math Short Reads
> >
> >
> > This textbook is the companion guide book to AP's Teaching True Mathematics, 1st year College. It is realized that Old Math will take a long time in removing their fake math, so in the interim period, this Guide book is designed to speed up the process of removing fake Calculus out of the education system, the fewer students we punish with forcing them with fake Calculus, the better we are.
> > Cover Picture: This book is part comedy, for when you cannot reason with math professors that they have many errors to fix, that 90% of their Calculus is in error, you end up resorting to comedy, making fun of them, to prod them to fix their errors. To prod them to "do right by the students of the world" not their entrenched propaganda.
> > Length: 54 pages
> >
> >
> > Product details
> > File Size: 1035 KB
> > Print Length: 64 pages
> > Simultaneous Device Usage: Unlimited
> > Publication Date: August 18, 2019
> > Sold by: Amazon.com Services LLC
> > Language: English
> > ASIN: B07WNGLQ85
> > Text-to-Speech: Enabled
> > X-Ray: Not Enabled
> > Word Wise: Not Enabled
> > Lending: Enabled
> > Enhanced Typesetting: Enabled
> > Amazon Best Sellers Rank: #253,425 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
> > #38 in 90-Minute Science & Math Short Reads
> > #318 in Calculus (Books)
> > #48 in Calculus (Kindle Store)
> >
> > #5-5, 72nd published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 4 for age 19-20 Sophomore-year College, math textbook series, book 5 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Preface: This is volume 4, book 5 of Teaching True Mathematics, designed for College Sophomore-year students, students of age 19-20. It is the continuation of volume 3 in the end-goal of learning how to do the mathematics of electricity and magnetism, because everything in physics is nothing but atoms and atoms are nothing but electricity and magnetism. To know math, you have to know physics. We learned the Calculus of 2nd dimension and applied it to the equations of physics for electricity and magnetism. But we did not learn the calculus of those equations for 3rd dimension. So, you can say that Sophomore year College math is devoted to 3D Calculus. This sophomore year college we fill in all the calculus, and we start over on all of Geometry, for geometry needs a modern day revision. And pardon me for this book is mostly reading, and the students doing less calculations. The classroom of this textbook has the teacher go through page by page to get the students comprehending and understanding of what is being taught. There are many hands on experiments also.
> >
> > Cover Picture shows some toruses, some round some square, torus of rings, thin strips of rings or squares and shows them laid flat. That is Calculus of 3rd dimension that lays a ring in a torus to be flat in 2nd dimension.
> > Length: 105 pages
> >
> > Product details
> > • ASIN : B0828M34VL
> > • Publication date : December 2, 2019
> > • Language : English
> > • File size : 952 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 105 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #242,037 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #36 in Calculus (Kindle Store)
> > ◦ #219 in Calculus (Books)
> >
> >
> > #5-6, 75th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 5 for age 20-21 Junior-year of College, math textbook series, book 6 Kindle Edition
> > by Archimedes Plutonium 2019
> >
> > This is volume 5, book 6 of Teaching True Mathematics, designed for College Junior-year students, students of age 20-21. In first year college Calculus we learned calculus of the 2nd dimension and applied it to the equations of physics for electricity and magnetism. And in sophomore year we learned calculus of 3rd dimension to complete our study of the mathematics needed to do the physics of electricity and magnetism. Now, junior year college, we move onto something different, for we focus mostly on logic now and especially the logic of what is called the "mathematical proof". Much of what the student has learned about mathematics so far has been given to her or him as stated knowledge, accept it as true because I say so. But now we are going to do math proofs. Oh, yes, we did prove a few items here and there, such as why the Decimal Grid Number system is so special, such as the Pythagorean Theorem, such as the Fundamental Theorem of Calculus with its right-triangle hinged up or down. But many ideas we did not prove, we just stated them and expected all students to believe them true. And you are now juniors in college and we are going to start to prove many of those ideas and teach you "what is a math proof". Personally, I myself feel that the math proof is overrated, over hyped. But the math proof is important for one reason-- it makes you better scientists of knowing what is true and what is a shaky idea. A math proof is the same as "thinking straight and thinking clearly". And all scientists need to think straight and think clearly. But before we get to the Mathematics Proof, we have to do Probability and Statistics. What you learned in Grade School, then High School, then College, called Sigma Error, now becomes Probability and Statistics. It is important because all sciences including mathematics needs and uses Probability and Statistics. So, our job for junior-year of college mathematics is all cut out and ahead for us, no time to waste, let us get going.
> >
> > Cover Picture: is a sample of the Array Proof, a proof the ellipse is not a conic but rather a cylinder cut wherein the oval is the slant cut of a cone, not the ellipse.
> >
> > Length: 175 pages
> >
> >
> > Product details
> > ASIN : B0836F1YF6
> > Publication date : December 26, 2019
> > Language : English
> > File size : 741 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 175 pages
> > Lending : Enabled
> > Best Sellers Rank: #3,768,255 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3,591 in Probability & Statistics (Kindle Store)
> > ◦ #19,091 in Probability & Statistics (Books)
> >
> >
> >
> > #5-7, 89th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 6 for age 21-22 Senior-year of College, math textbook series, book 7 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revision was 6Feb2021.
> > Preface: This is the last year of College for mathematics and we have to mostly summarize all of mathematics as best we can. And set a new pattern to prepare students going on to math graduate school. A new pattern of work habits, because graduate school is more of research and explore on your own. So in this final year, I am going to eliminate tests, and have it mostly done as homework assignments.
> >
> > Cover Picture: Again and again, many times in math, the mind is not good enough alone to think straight and clear, and you need tools to hands-on see how it works. Here is a collection of tools for this senior year college classes. There is a pencil, clipboard, graph paper, compass, divider, protractor, slide-ruler. And for this year we spend a lot of time on the parallelepiped, showing my wood model, and showing my erector set model held together by wire loops in the corners. The plastic square is there only to hold up the erector set model.
> >
> > Length: 110 pages
> >
> > Product details
> > ASIN : B084V11BGY
> > Publication date : February 15, 2020
> > Language : English
> > File size : 826 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Enabled
> > Print length : 110 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,965 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #345 in Mathematics (Kindle Store)
> > ◦ #373 in Physics (Kindle Store)
> > ◦ #2,256 in Physics (Books)
> >
> > #5-8, 90th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 7 for age 22-26 Graduate school, math textbook series, book 8 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revised 1NOV2020. This was AP's 90th published book of science.
> >
> > Preface: This is College Graduate School mathematics. Congratulations, you made it this far. To me, graduate school is mostly research, research mathematics and that means also physics. So it is going to be difficult to do math without physics. Of course, we focus on the mathematics of these research projects.
> >
> > My textbook for Graduate school is just a template and the professors teaching the graduate students are free of course to follow their own projects, but in terms of being physics and math combined. What I list below is a template for possible projects.
> >
> > So, in the below projects, I list 36 possible research projects that a graduate student my like to undertake, or partake. I list those 36 projects with a set of parentheses like this (1), (2), (3), etc. Not to be confused with the chapters listing as 1), 2), 3), etc. I list 36 projects but the professor can offer his/her own list, and I expect students with their professor, to pick a project and to monitor the student as to his/her progresses through the research. I have listed each project then cited some of my own research into these projects, below each project is an entry. Those entries are just a help or helper in getting started or acquainted with the project. The entry has a date time group and a newsgroup that I posted to such as sci.math or plutonium-atom-universe Google newsgroups. Again the entry is just a help or helper in getting started.
> >
> > Now instead of picking one or two projects for your Graduate years of study, some may select all 36 projects where you write a short paper on each project. Some may be bored with just one or two projects and opt for all 36.
> >
> > Cover Picture: A photo by my iphone of a page on Permutations of the Jacobs book Mathematics: A Human Endeavor, 1970. One of the best textbooks ever written in Old Math, not for its contents because there are many errors, but for its teaching style. It is extremely rare to find a math textbook written for the student to learn. Probably because math professors rarely learned how to teach in the first place; only learned how to unintentionally obfuscate. The page I photographed is important because it is the interface between geometry's perimeter or surface area versus geometry's area or volume, respectively. Or, an interface of pure numbers with that of geometry. But I have more to say on this below.
> > Length: 296 pages
> >
> > Product details
> > ASIN : B085DF8R7V
> > Publication date : March 1, 2020
> > Language : English
> > File size : 828 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 296 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,981 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #13 in General Geometry
> > ◦ #213 in Geometry & Topology (Books)
> >
> >
> >
> > #5-8, 160th published book
> >
> > MATHOPEDIA-- List of 80 fakes and mistakes of Old Math// Student teaches professor Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 28Apr2022. And this is AP's 160th book of Science.
> > Preface:
> > A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.
> > The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.
> > The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery. I know because I have been there.
> > Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.
> > I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).
> >
> > Product details
> > • ASIN : B09MZTLRL5
> > • Publication date : December 2, 2021
> > • Language : English
> > • File size : 1149 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 65 pages
> > • Lending : Enabled
Dan Christensen
Nov 21, 2022, 10:41:20 PM11/21/22
to
Silly old Archie Poo! I see you have deleted and then REPOSTED the VERY SAME misinformation and lies. Why would you do that???
Blake Armanni
Nov 22, 2022, 9:04:14 AM11/22/22
to
Dan Christensen wrote:
> STUDENTS BEWARE: Don't be a victim of AP's fake math and science
>
> On Monday, November 21, 2022 at 5:37:02 PM UTC-5, Archimedes Plutonium
> wrote:
>> >Dan Christensen ...
>
> STUDENTS BEWARE: Don't be a victim of AP's fake math and science
the many times proven terrorists, and *_state_driven_terrorist_* are
> STUDENTS BEWARE: Don't be a victim of AP's fake math and science
>
> On Monday, November 21, 2022 at 5:37:02 PM UTC-5, Archimedes Plutonium
> wrote:
>> >Dan Christensen ...
>
> STUDENTS BEWARE: Don't be a victim of AP's fake math and science
demanding OTHERS to be named "terrorist". The people defending their
people from be killed by the nazis, has to named "terrorists".
as is written in The Bible, without bombs over their stupid heads, these
khazar goy of the west will NOT stop their despicable lying. These
modrafaka are born with bifurcated tongues. Braindead and with bifurcated
tongue. Drive a family with grandparents and children, in such world of
lying bitches. You can't. The bifurcated tongue lying bitches are wanting
to kill you.
NATO assembly urges members to declare Russia ‘terrorist regime’
https://%72%74.com/news/566965-nato-russia-terrorist-regime/
Dan Christensen
Nov 22, 2022, 12:37:09 PM11/22/22
to
On Tuesday, November 22, 2022 at 9:04:14 AM UTC-5, Blake Armanni wrote:
> Dan Christensen wrote:
>
> > STUDENTS BEWARE: Don't be a victim of AP's fake math and science
> >
> > On Monday, November 21, 2022 at 5:37:02 PM UTC-5, Archimedes Plutonium
> > wrote:
> >> >Dan Christensen ...
> >
> > STUDENTS BEWARE: Don't be a victim of AP's fake math and science
> the many times proven terrorists, and *_state_driven_terrorist_* ...
> Dan Christensen wrote:
>
> > STUDENTS BEWARE: Don't be a victim of AP's fake math and science
> >
> > On Monday, November 21, 2022 at 5:37:02 PM UTC-5, Archimedes Plutonium
> > wrote:
> >> >Dan Christensen ...
> >
> > STUDENTS BEWARE: Don't be a victim of AP's fake math and science
Hey, Nazi Boy, how's Putin's genocidal war of conquest and terror going for you? That Red Army of yours sure ain't what it used to be! XAXAXA
Dudley Brooks
Nov 22, 2022, 4:25:43 PM11/22/22
to
this proof, works. It has to do with the rules of logic pertaining to
the naming of variables. In a nutshell, the name of a variable is
arbitrary, and can be changed at will, as long as it is done
consistently throughout the entire proof and is not the same as the name
of some other variable in the proof. (IIRC, that's a corollary of a
theorem in Proof Theory, about substitution.)
This proof uses no properties whatsoever of redness and blueness, so
"red" and "blue" are merely the arbitrary names of two variables and are
(ex)changeable at will. So the "red proof" and the "blue proof" are not
merely analogous, they are literally the same proof, and there's no
reason to say it twice. (It would be like saying that a proof in
English and the same proof in French are two different proofs.)
--
Dudley Brooks, Artistic Director
Run For Your Life! ... it's a dance company!
San Francisco
Dan Christensen
Nov 22, 2022, 4:47:11 PM11/22/22
to
Dudley Brooks
Nov 22, 2022, 7:54:24 PM11/22/22
to
Once you have (formally) proved in Proof Theory that the names of
variables can be changed, you don't have prove *that* as part of every
subsequent proof! In other words, it is completely unnecessary to prove
(formally or otherwise) the "symmetry" -- the one proof is the
*translation* of the other.
So I still insist that the two proofs are not symmetrical ... they are
*identical* -- they are literally the same proof! Just imagine that
there are two languages. In one the color of blood is called "red" and
the color of the sky is called "blue", and in the other the color of
blood is called "blue" and the color of the sky is called "red". Two
speakers are giving the proof in their respective languages. Each
speaker says "Assume, WLOG, that the first object is <insert respective
word for the color of blood here>." I say they are giving *exactly the
same proof*.
Or, borrowing two words from a famous philosophy discussion, suppose the
problem is "If three objects are each painted either bleen or grue, then
there must be at least two objects of the same color." A different
problem? Really???
The formal theorem behind this goes something like this (I haven't done
this since about 1966, so it's from memory, and I don't want to take the
time to look it up):
"If P(x,y,z,...) |- q(x,y,z,...) then P(x/t,y,z,...) |- q(x/t,y,z,...),
where t is none of y,z,..."
Here, P is a set of axioms and previously proved theorems, q is some new
theorem, "|-" means "syntactically yields" (i.e. you can formally prove
q from P), x,y,z,... are the variables in the statements of the axioms
and theorems, and "x/t" means "with every occurrence of x replaced with
t." Since q can be *any* theorem, that's why you're always justified in
simply replacing one name with another. All you have to do is *notice*
that one name has been replaced with another. The "proof" of the
replacement ia "see for yourself!"
Speaking of English proofs and French proofs: One of my jobs when I
worked for a math textbook company was translating a book of math
competition problems and their solutions from French to English. Even
though the book's blurb promised that all solutions (including proofs)
were extremely detailed, one particular problem only gave a very sketchy
"hand-wavy" proof. So I decide to completely re-write that proof ...
using a new method in the process. That expanded it from a paragraph to
several pages ... which still left a few things somewhat glossed over,
that's how much harder that problem was than the others in the book!
So in that case, the French proof and the English proof were completely
different! ;^)
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
Dudley Brooks
Nov 22, 2022, 9:11:22 PM11/22/22
to
Hi, Dan --
Since I'm always afraid of unintentionally giving offense, I just want
to say that I didn't intended my perhaps over-explained response to come
across like I was casting any aspersions on your qualifications or
knowledge. I'm aware of, and appreciative of, your theorem-proving
software.
It's just that since we were talking about formal proofs, I decided to
be somewhat formal! ;^)
Since I'm always afraid of unintentionally giving offense, I just want
to say that I didn't intended my perhaps over-explained response to come
across like I was casting any aspersions on your qualifications or
knowledge. I'm aware of, and appreciative of, your theorem-proving
software.
It's just that since we were talking about formal proofs, I decided to
be somewhat formal! ;^)
Dan Christensen
Nov 22, 2022, 11:06:21 PM11/22/22
to
On Tuesday, November 22, 2022 at 7:54:24 PM UTC-5, Dudley Brooks wrote:
[snip]
> >> There's a very good justification of why "WLOG", at least of the kind in
> >> this proof, works. It has to do with the rules of logic pertaining to
> >> the naming of variables. In a nutshell, the name of a variable is
> >> arbitrary, and can be changed at will, as long as it is done
> >> consistently throughout the entire proof and is not the same as the name
> >> of some other variable in the proof. (IIRC, that's a corollary of a
> >> theorem in Proof Theory, about substitution.)
> >>
> >> This proof uses no properties whatsoever of redness and blueness, so
> >> "red" and "blue" are merely the arbitrary names of two variables and are
> >> (ex)changeable at will. So the "red proof" and the "blue proof" are not
> >> merely analogous, they are literally the same proof, and there's no
> >> reason to say it twice. (It would be like saying that a proof in
> >> English and the same proof in French are two different proofs.)
> >
> > That all works very nicely for informal proofs presented to a knowledgeable audience. If, however, you are writing formal proofs, it may well not be worth the effort to formally prove the symmetry of the proof. (Don't know how you would do that.) It would probably be easier to simply go through each case, tediously changing the names of variables, etc.. :^(
> Invoking a theorem of Proof Theory sounds to me like a formal proof!
> Once you have (formally) proved in Proof Theory that the names of
> variables can be changed, you don't have prove *that* as part of every
> subsequent proof! In other words, it is completely unnecessary to prove
> (formally or otherwise) the "symmetry" -- the one proof is the
> *translation* of the other.
>
> So I still insist that the two proofs are not symmetrical ... they are
> *identical* -- they are literally the same proof!
[snip]
A careful, line-by-line comparison will show that there a small differences in the text, more than those resulting from simply interchanging "red" and "blue." Compare Sub-proof 1 (lines 32-63) and Sub-proof 2 (lines 64-95) . Compare the even the the 3rd lines of each:
34 color(x)=color(y)
Substitute, 33, 32
...
66. color(z)=red
Premise
My point is that it would probably take more effort to formally prove these sub-proofs are somehow logically equivalent than it would be to just consider each case in turn. I wouldn't know where to begin!
[snip]
> >> There's a very good justification of why "WLOG", at least of the kind in
> >> this proof, works. It has to do with the rules of logic pertaining to
> >> the naming of variables. In a nutshell, the name of a variable is
> >> arbitrary, and can be changed at will, as long as it is done
> >> consistently throughout the entire proof and is not the same as the name
> >> of some other variable in the proof. (IIRC, that's a corollary of a
> >> theorem in Proof Theory, about substitution.)
> >>
> >> This proof uses no properties whatsoever of redness and blueness, so
> >> "red" and "blue" are merely the arbitrary names of two variables and are
> >> (ex)changeable at will. So the "red proof" and the "blue proof" are not
> >> merely analogous, they are literally the same proof, and there's no
> >> reason to say it twice. (It would be like saying that a proof in
> >> English and the same proof in French are two different proofs.)
> >
> > That all works very nicely for informal proofs presented to a knowledgeable audience. If, however, you are writing formal proofs, it may well not be worth the effort to formally prove the symmetry of the proof. (Don't know how you would do that.) It would probably be easier to simply go through each case, tediously changing the names of variables, etc.. :^(
> Invoking a theorem of Proof Theory sounds to me like a formal proof!
> Once you have (formally) proved in Proof Theory that the names of
> variables can be changed, you don't have prove *that* as part of every
> subsequent proof! In other words, it is completely unnecessary to prove
> (formally or otherwise) the "symmetry" -- the one proof is the
> *translation* of the other.
>
> So I still insist that the two proofs are not symmetrical ... they are
> *identical* -- they are literally the same proof!
A careful, line-by-line comparison will show that there a small differences in the text, more than those resulting from simply interchanging "red" and "blue." Compare Sub-proof 1 (lines 32-63) and Sub-proof 2 (lines 64-95) . Compare the even the the 3rd lines of each:
34 color(x)=color(y)
Substitute, 33, 32
...
66. color(z)=red
Premise
My point is that it would probably take more effort to formally prove these sub-proofs are somehow logically equivalent than it would be to just consider each case in turn. I wouldn't know where to begin!
Dan Christensen
Nov 22, 2022, 11:17:07 PM11/22/22
to
On Tuesday, November 22, 2022 at 9:11:22 PM UTC-5, Dudley Brooks wrote:
> Hi, Dan --
>
> Since I'm always afraid of unintentionally giving offense, I just want
> to say that I didn't intended my perhaps over-explained response to come
> across like I was casting any aspersions on your qualifications or
> knowledge. I'm aware of, and appreciative of, your theorem-proving
> software.
>
Absolutely NO offense taken!
> Hi, Dan --
>
> Since I'm always afraid of unintentionally giving offense, I just want
> to say that I didn't intended my perhaps over-explained response to come
> across like I was casting any aspersions on your qualifications or
> knowledge. I'm aware of, and appreciative of, your theorem-proving
> software.
>
BTW don't confuse me with my illustrious namesake at Western U. I'm just a hobbyist. No post-grad degrees. But the software is mine.
Ross A. Finlayson
Nov 23, 2022, 12:52:39 AM11/23/22
to
Ross A. Finlayson
Nov 23, 2022, 7:30:37 AM11/23/22
to
It goes without saying it's like "sine qua non", it goes without saying.
Obviously, it's obviously.
Sometimes it's ironic or oxymoronic, branch-picking loss-of-generality.
Euh, your field's not closed, if you do or don't look back.
We have a pure formal system, about tautology and isochrony. It's general.
FromTheRafters
Nov 23, 2022, 7:35:44 AM11/23/22
to
Dudley Brooks wrote:
> On 11/22/22 1:47 PM, Dan Christensen wrote:
>
> say they are giving *exactly the same proof*.
>
> Or, borrowing two words from a famous philosophy discussion, suppose the
> problem is "If three objects are each painted either bleen or grue, then
> there must be at least two objects of the same color." A different problem?
> Really???
Looks like a minimal (or generalized?) pigeonhole principle to me.
> On 11/22/22 1:47 PM, Dan Christensen wrote:
>
> say they are giving *exactly the same proof*.
>
> Or, borrowing two words from a famous philosophy discussion, suppose the
> problem is "If three objects are each painted either bleen or grue, then
> there must be at least two objects of the same color." A different problem?
> Really???
Marquis Franco
Nov 23, 2022, 7:58:48 AM11/23/22
to
Dan Christensen wrote:
> On Tuesday, November 22, 2022 at 9:11:22 PM UTC-5, Dudley Brooks wrote:
>> Hi, Dan -- Since I'm always afraid of unintentionally giving offense, I
>
> On Tuesday, November 22, 2022 at 9:11:22 PM UTC-5, Dudley Brooks wrote:
>> Hi, Dan -- Since I'm always afraid of unintentionally giving offense, I
>
> Absolutely NO offense taken!
> BTW don't confuse me with my illustrious namesake at Western U. I'm just
> a hobbyist. No post-grad degrees. But the software is mine.
then yet another solid proof your *_terrorist_government_* wants to kill
> BTW don't confuse me with my illustrious namesake at Western U. I'm just
> a hobbyist. No post-grad degrees. But the software is mine.
you. They are capitalist philanthrops. They give you "vaccines" for free.
And a burger with french fries.
Died Suddenly.
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/w3C5OR5Niyir
repeat after me *govern* - *_M_E_N_T_*. Make it ten times. And you just
don't call your wive *Michael* by "mistake".
Danish Prime Minister is confronted by citizen about the death toll and
injuries caused by the jabs
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/rFejtc10miY0
Justine Caito
Nov 23, 2022, 8:17:21 AM11/23/22
to
Dan Christensen wrote:
> On Tuesday, November 22, 2022 at 7:54:24 PM UTC-5, Dudley Brooks wrote:
>> So I still insist that the two proofs are not symmetrical ... they are
>> *identical* -- they are literally the same proof! [snip]
>
> A careful, line-by-line comparison will show that there a small
> differences in the text, more than those resulting from simply
give me a break, you terrorists are terrorizing the world calling your
> On Tuesday, November 22, 2022 at 7:54:24 PM UTC-5, Dudley Brooks wrote:
>> So I still insist that the two proofs are not symmetrical ... they are
>> *identical* -- they are literally the same proof! [snip]
>
> A careful, line-by-line comparison will show that there a small
> differences in the text, more than those resulting from simply
wives *Michel* by "mistake". For fuck sake, these wankers philanthrops are
terrorizing the planet with *vaccines* and *death_panels*.
the idiots thinking "vaccines" are "good", are idiots. Any vaccine. That's
how they kill your family, short_term, long_term.
Heads up! Have you heard about ＂Death Panels＂ that will get to decide if
you live or die
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/JHdWYKSj68MF
MICHELLE OBAMA IS A MAN
https://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/nGLJ2HiJgIst/
Ross A. Finlayson
Nov 23, 2022, 8:54:55 AM11/23/22
to
Dan Christensen
Nov 23, 2022, 10:32:05 AM11/23/22
to
On Wednesday, November 23, 2022 at 7:58:48 AM UTC-5, Marquis Franco wrote:
> Dan Christensen wrote:
>
> > On Tuesday, November 22, 2022 at 9:11:22 PM UTC-5, Dudley Brooks wrote:
> >> Hi, Dan -- Since I'm always afraid of unintentionally giving offense, I
> >
> > Absolutely NO offense taken!
> > BTW don't confuse me with my illustrious namesake at Western U. I'm just
> > a hobbyist. No post-grad degrees. But the software is mine.
> then yet another solid proof your *_terrorist_government_* wants to kill
> you.
So, naZee Boy (is that what the "Z" stand for?), it seems you have not volunteered to be cannon fodder in Putin's genocidal war of conquest and terror in Ukraine. Perhaps the one smart thing you have done in your life. Now, you really must go into hiding. Like the original Nazis, you are on the wrong side of history.
> Dan Christensen wrote:
>
> > On Tuesday, November 22, 2022 at 9:11:22 PM UTC-5, Dudley Brooks wrote:
> >> Hi, Dan -- Since I'm always afraid of unintentionally giving offense, I
> >
> > Absolutely NO offense taken!
> > BTW don't confuse me with my illustrious namesake at Western U. I'm just
> > a hobbyist. No post-grad degrees. But the software is mine.
> then yet another solid proof your *_terrorist_government_* wants to kill
> you.
Baesmarc Ungaretti
Nov 23, 2022, 10:53:51 AM11/23/22
to
Dan Christensen wrote:
>> > Absolutely NO offense taken!
>> > BTW don't confuse me with my illustrious namesake at Western U. I'm
>> > just a hobbyist. No post-grad degrees. But the software is mine.
>> then yet another solid proof your *_terrorist_government_* wants to
>> kill you.
>
> So, naZee Boy (is that what the "Z" stand for?), it seems you have not
> volunteered to be cannon fodder in Putin's genocidal war of conquest and
> terror in Ukraine. Perhaps the one smart thing you have done in your
> life. Now, you really must go into hiding. Like the original Nazis, you
> are on the wrong side of history.
you can't fucking read. You neither undrestand history. You are calling
>> > Absolutely NO offense taken!
>> > BTW don't confuse me with my illustrious namesake at Western U. I'm
>> > just a hobbyist. No post-grad degrees. But the software is mine.
>> then yet another solid proof your *_terrorist_government_* wants to
>> kill you.
>
> So, naZee Boy (is that what the "Z" stand for?), it seems you have not
> volunteered to be cannon fodder in Putin's genocidal war of conquest and
> terror in Ukraine. Perhaps the one smart thing you have done in your
> life. Now, you really must go into hiding. Like the original Nazis, you
> are on the wrong side of history.
your wive *Michael* by mistake? And you ate the burger and the french
fries.
then yet another solid proof your *_terrorist_government_* wants to kill
Mostowski Collapse
Nov 23, 2022, 11:03:51 AM11/23/22
to
Micro penis aka Luigi, que fa?
Kids React to Luigi Death Stare
https://www.youtube.com/watch?v=HOpKUrE9eKU
Mostowski Collapse
Nov 23, 2022, 11:22:23 AM11/23/22
to
Lets keep Wonky Man busy with a new contraption.
Yeah, this is not some "without loss" heuristic applied,
you proof two theorems, and then join them:
96 [color(x)=red
=> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
& [color(x)=blue
=> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
Join, 63, 95
https://www.dcproof.com/WithoutLossOfGenerality.htm
The proof SUB-PROOF 1 and the proof SUB-PROOF 2 are
the same proof twice. If you need to prove:
a v b -> c
And if thee is a Galois connection (F,G), such that
F(a)<->b and G(c)<->c, its enought to prove:
https://en.wikipedia.org/wiki/Galois_connection
a -> c
LoL
Proof: a -> c, is the same as a -> c, since G(c) <-> c.
Therefore we have also a proof a -> G(c). Now by
definition of Galois connection, there is also a proof
F(a) -> c, but we have F(a) <-> b, so there is a proof
b -> c, and now we can use v introduction rule:
a -> c
b -> c
----------------- (v-Intro)
a v b -> c
Yeah, this is not some "without loss" heuristic applied,
you proof two theorems, and then join them:
96 [color(x)=red
=> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
& [color(x)=blue
=> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
Join, 63, 95
https://www.dcproof.com/WithoutLossOfGenerality.htm
The proof SUB-PROOF 1 and the proof SUB-PROOF 2 are
the same proof twice. If you need to prove:
a v b -> c
And if thee is a Galois connection (F,G), such that
F(a)<->b and G(c)<->c, its enought to prove:
https://en.wikipedia.org/wiki/Galois_connection
a -> c
LoL
Proof: a -> c, is the same as a -> c, since G(c) <-> c.
Therefore we have also a proof a -> G(c). Now by
definition of Galois connection, there is also a proof
F(a) -> c, but we have F(a) <-> b, so there is a proof
b -> c, and now we can use v introduction rule:
a -> c
b -> c
----------------- (v-Intro)
a v b -> c
Dan Christensen
Nov 23, 2022, 12:06:14 PM11/23/22
to
On Wednesday, November 23, 2022 at 11:22:23 AM UTC-5, Mostowski Collapse wrote:
> Lets keep Wonky Man busy with a new contraption.
> Yeah, this is not some "without loss" heuristic applied,
> you proof two theorems, and then join them:
>
> 96 [color(x)=red
> => EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
> & [color(x)=blue
> => EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
> Join, 63, 95
> https://www.dcproof.com/WithoutLossOfGenerality.htm
>
> The proof SUB-PROOF 1 and the proof SUB-PROOF 2 are
> the same proof twice.
[snip]
> Lets keep Wonky Man busy with a new contraption.
> Yeah, this is not some "without loss" heuristic applied,
> you proof two theorems, and then join them:
>
> 96 [color(x)=red
> => EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
> & [color(x)=blue
> => EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]]
> Join, 63, 95
> https://www.dcproof.com/WithoutLossOfGenerality.htm
>
> The proof SUB-PROOF 1 and the proof SUB-PROOF 2 are
> the same proof twice.
You will need a simple formal proof to somehow establish the "symmetry" of Sub-Proof 1, and then another simple formal proof to apply that result to obtain the required result for the second case (i.e. for color(x)=blue). You would STILL need line 96 though. Somehow, I don't think you will find all this to be a "shortcut," Jan Burse. Quite the contrary.
Ross A. Finlayson
Nov 23, 2022, 12:11:33 PM11/23/22
to
Dan Christensen
Nov 23, 2022, 12:52:20 PM11/23/22
to
Mostowski Collapse
Nov 23, 2022, 3:30:37 PM11/23/22
to
Thats rather easy, the Galois connection is a permutation, of the colors.
The only non-identity permutation of two colors is swapping them.
So lets write the desired theorem with the colors as additional
parameters, namely:
C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
Now you prove:
ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
Then you can conclude:
ALL(red):ALL(blue):(x=blue => C(red,blue))
Here my claim verified by Wolfgang Schwartz tool:
(∀r∀b(x=r → Crbxyz) ∧ ∀r∀b(Crbxyz → Cbrxyz)) → ∀r∀b(x=b → Crbxyz) is valid.
https://www.umsu.de/trees/#~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~1~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6r~6b%28x=b~5C%28r,b,x,y,z%29%29
The only non-identity permutation of two colors is swapping them.
So lets write the desired theorem with the colors as additional
parameters, namely:
C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
Now you prove:
ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
Then you can conclude:
ALL(red):ALL(blue):(x=blue => C(red,blue))
Here my claim verified by Wolfgang Schwartz tool:
(∀r∀b(x=r → Crbxyz) ∧ ∀r∀b(Crbxyz → Cbrxyz)) → ∀r∀b(x=b → Crbxyz) is valid.
https://www.umsu.de/trees/#~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~1~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6r~6b%28x=b~5C%28r,b,x,y,z%29%29
Mostowski Collapse
Nov 23, 2022, 4:01:03 PM11/23/22
to
Credits for using this Galois Connection go to:
Dudley Brooks schrieb am Dienstag, 22. November 2022 um 22:25:43 UTC+1:
> [...] It has to do with the rules of logic pertaining to
> Dudley Brooks, Artistic Director
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/nw6dfej-BQAJ
Lets make the Galois Connection (F,G) transparent. If
we swap red and blue, then lets says that is the F functor.
The G functor is the same functor again, since swapping
is its own inverse permutation. Now first verify the
fixpoint, G(c) <-> c, we assume that we can show:
ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
From it, it follows:
ALL(red):ALL(blue):(C(blue,red,x,y,z) => C(red,blue,x,y,z))
Verifiable with Wolfgang Schwartz tool:
∀r∀b(Crbxyz → Cbrxyz) → ∀r∀b(Cbrxyz → Crbxyz) is valid.
https://www.umsu.de/trees/#~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6r~6b%28C%28b,r,x,y,z%29~5C%28r,b,x,y,z%29%29
So that we have indeed:
ALL(red):ALL(blue):(C(blue,red,x,y,z) <=> C(red,blue,x,y,z))
The rest is also as in the Galois Connection criterias,
namely F(a) <-> b. We did already F(a) -> b, using c -> G(c),
now that we also have G(c) -> c, we will be able to show b -> F(a).
Whats a little messy here the quantifiers are sometimes
outside of -> and sometimes inside the arguments of ->.
But don't worry, we can show:
∀r∀bC(r,b,x,y,z) → ∀r∀b(C(r,b,x,y,z) → C(b,r,x,y,z))
https://www.umsu.de/trees/#~6r~6bC%28r,b,x,y,z%29~5~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29
So maybe should rework everything to arrive at a less
sloppy presentation
Dudley Brooks schrieb am Dienstag, 22. November 2022 um 22:25:43 UTC+1:
> [...] It has to do with the rules of logic pertaining to
> the naming of variables. In a nutshell, the name of a variable is
> arbitrary, and can be changed at will, as long as it is done
> consistently throughout the entire proof and is not the same as the name
> of some other variable in the proof. (IIRC, that's a corollary of a
> theorem in Proof Theory, about substitution.) [...]
> arbitrary, and can be changed at will, as long as it is done
> consistently throughout the entire proof and is not the same as the name
> of some other variable in the proof. (IIRC, that's a corollary of a
> Dudley Brooks, Artistic Director
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/nw6dfej-BQAJ
Lets make the Galois Connection (F,G) transparent. If
we swap red and blue, then lets says that is the F functor.
The G functor is the same functor again, since swapping
is its own inverse permutation. Now first verify the
fixpoint, G(c) <-> c, we assume that we can show:
ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
ALL(red):ALL(blue):(C(blue,red,x,y,z) => C(red,blue,x,y,z))
Verifiable with Wolfgang Schwartz tool:
∀r∀b(Crbxyz → Cbrxyz) → ∀r∀b(Cbrxyz → Crbxyz) is valid.
https://www.umsu.de/trees/#~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6r~6b%28C%28b,r,x,y,z%29~5C%28r,b,x,y,z%29%29
So that we have indeed:
ALL(red):ALL(blue):(C(blue,red,x,y,z) <=> C(red,blue,x,y,z))
The rest is also as in the Galois Connection criterias,
namely F(a) <-> b. We did already F(a) -> b, using c -> G(c),
now that we also have G(c) -> c, we will be able to show b -> F(a).
Whats a little messy here the quantifiers are sometimes
outside of -> and sometimes inside the arguments of ->.
But don't worry, we can show:
∀r∀bC(r,b,x,y,z) → ∀r∀b(C(r,b,x,y,z) → C(b,r,x,y,z))
https://www.umsu.de/trees/#~6r~6bC%28r,b,x,y,z%29~5~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29
So maybe should rework everything to arrive at a less
sloppy presentation
Message has been deleted
Dan Christensen
Nov 23, 2022, 4:10:54 PM11/23/22
to
On Wednesday, November 23, 2022 at 3:30:37 PM UTC-5, Mostowski Collapse wrote:
> Thats rather easy, the Galois connection is a permutation, of the colors.
> The only non-identity permutation of two colors is swapping them.
>
> So lets write the desired theorem with the colors as additional
> parameters, namely:
>
Hint: Your first 63 lines will be the same as mine. Then what? What is your line 64? What about 64 and 65? Get back to us when you have at least that much.
> Thats rather easy, the Galois connection is a permutation, of the colors.
> The only non-identity permutation of two colors is swapping them.
>
> So lets write the desired theorem with the colors as additional
> parameters, namely:
>
> Thats rather easy, the Galois connection is a permutation, of the colors.
> The only non-identity permutation of two colors is swapping them.
>
> So lets write the desired theorem with the colors as additional
> parameters, namely:
>
What part of FORMAL PROOF don't you understand, Jan Burse. OK let's take one line at at time.
> The only non-identity permutation of two colors is swapping them.
>
> So lets write the desired theorem with the colors as additional
> parameters, namely:
>
Hint: Your first 63 lines will be the same as mine. Then what? What is your line 64? What about 65 and 66? Get back to us when you have at least that much.
Mostowski Collapse
Nov 23, 2022, 4:31:47 PM11/23/22
to
Well we only prove SUB-PROOF 1 , but we don't prove SUB-PROOF 2.
Its a consequence:
Mostowski Collapse schrieb am Mittwoch, 23. November 2022 um 21:30:37 UTC+1:
> Now you prove:
>
> ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
> ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
>
> Then you can conclude:
>
> ALL(red):ALL(blue):(x=blue => C(red,blue,x,y,z))
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/P_feO3tKBgAJ
Too hard to understand what WLOG means for Wonky Man?
Its a consequence:
Mostowski Collapse schrieb am Mittwoch, 23. November 2022 um 21:30:37 UTC+1:
> Now you prove:
>
> ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
> ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
>
> Then you can conclude:
>
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/P_feO3tKBgAJ
Too hard to understand what WLOG means for Wonky Man?
Dan Christensen
Nov 23, 2022, 4:50:52 PM11/23/22
to
On Wednesday, November 23, 2022 at 4:31:47 PM UTC-5, Mostowski Collapse wrote:
> Mostowski Collapse schrieb am Mittwoch, 23. November 2022 um 21:30:37 UTC+1:
> > Now you prove:
> >
> > ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
> > ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
> >
> > Then you can conclude:
> >
> > ALL(red):ALL(blue):(x=blue => C(red,blue,x,y,z))
> https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/P_feO3tKBgAJ
>
> Too hard to understand what WLOG means for Wonky Man?
> Dan Christensen schrieb am Mittwoch, 23. November 2022 um 22:10:54 UTC+1:
> > On Wednesday, November 23, 2022 at 3:30:37 PM UTC-5, Mostowski Collapse wrote:
> > > Thats rather easy, the Galois connection is a permutation, of the colors.
> > > The only non-identity permutation of two colors is swapping them.
> > >
> > > So lets write the desired theorem with the colors as additional
> > > parameters, namely:
> > >
> > Hint: Your first 63 lines will be the same as mine. Then what? What is your line 64? What about 64 and 65? Get back to us when you have at least that much.
> > > Thats rather easy, the Galois connection is a permutation, of the colors.
> > > The only non-identity permutation of two colors is swapping them.
> > >
> > > So lets write the desired theorem with the colors as additional
> > > parameters, namely:
> > >
> > What part of FORMAL PROOF don't you understand, Jan Burse. OK let's take one line at at time.
> >
> > Hint: Your first 63 lines will be the same as mine. Then what? What is your line 64? What about 65 and 66? Get back to us when you have at least that much.
> Well we only prove SUB-PROOF 1 , but we don't prove SUB-PROOF 2.
> Its a consequence
[snip]
> Mostowski Collapse schrieb am Mittwoch, 23. November 2022 um 21:30:37 UTC+1:
> > Now you prove:
> >
> > ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
> > ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
> >
> > Then you can conclude:
> >
> > ALL(red):ALL(blue):(x=blue => C(red,blue,x,y,z))
> https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/P_feO3tKBgAJ
>
> Too hard to understand what WLOG means for Wonky Man?
> Dan Christensen schrieb am Mittwoch, 23. November 2022 um 22:10:54 UTC+1:
> > On Wednesday, November 23, 2022 at 3:30:37 PM UTC-5, Mostowski Collapse wrote:
> > > Thats rather easy, the Galois connection is a permutation, of the colors.
> > > The only non-identity permutation of two colors is swapping them.
> > >
> > > So lets write the desired theorem with the colors as additional
> > > parameters, namely:
> > >
> > Hint: Your first 63 lines will be the same as mine. Then what? What is your line 64? What about 64 and 65? Get back to us when you have at least that much.
> > > Thats rather easy, the Galois connection is a permutation, of the colors.
> > > The only non-identity permutation of two colors is swapping them.
> > >
> > > So lets write the desired theorem with the colors as additional
> > > parameters, namely:
> > >
> > What part of FORMAL PROOF don't you understand, Jan Burse. OK let's take one line at at time.
> >
> > Hint: Your first 63 lines will be the same as mine. Then what? What is your line 64? What about 65 and 66? Get back to us when you have at least that much.
> Well we only prove SUB-PROOF 1 , but we don't prove SUB-PROOF 2.
> Its a consequence
So, you have no idea of what to do next, Jan Burse. You cannot even tell what the next line would be. Oh, well...
Dan
Mostowski Collapse
Nov 23, 2022, 4:53:50 PM11/23/22
to
But I made an error, I didn't quantify x, so this is better:
∀x∀y∀z∀r∀b(x=r → Crbxyz) →
(∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz) →
∀x∀y∀z∀b∀r(x=b → Cbrxyz)) is valid.
https://www.umsu.de/trees/#~6x~6y~6z~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~5~6x~6y~6z~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6x~6y~6z~6b~6r%28x=b~5C%28b,r,x,y,z%29%29
But this is only to illustrate why x=b case is redundant,
when we know something about permuation. We can now prove:
∀x∀y∀z∀r∀b(x=r → Crbxyz) →
(∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz) →
∀x∀y∀z∀b∀r((x=r ∨ x=b) → Crbxyz)) is valid.
https://www.umsu.de/trees/#~6x~6y~6z~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~5~6x~6y~6z~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6x~6y~6z~6b~6r%28x=r~2x=b~5C%28r,b,x,y,z%29%29
∀x∀y∀z∀r∀b(x=r → Crbxyz) →
(∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz) →
∀x∀y∀z∀b∀r(x=b → Cbrxyz)) is valid.
https://www.umsu.de/trees/#~6x~6y~6z~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~5~6x~6y~6z~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6x~6y~6z~6b~6r%28x=b~5C%28b,r,x,y,z%29%29
But this is only to illustrate why x=b case is redundant,
when we know something about permuation. We can now prove:
∀x∀y∀z∀r∀b(x=r → Crbxyz) →
(∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz) →
∀x∀y∀z∀b∀r((x=r ∨ x=b) → Crbxyz)) is valid.
https://www.umsu.de/trees/#~6x~6y~6z~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~5~6x~6y~6z~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6x~6y~6z~6b~6r%28x=r~2x=b~5C%28r,b,x,y,z%29%29
Mostowski Collapse
Nov 23, 2022, 5:02:49 PM11/23/22
to
Corr.: Actually we can formulate the redundancy,
only based on alpha-conversion of bounded quantifers:
∀x∀y∀z∀r∀b(x=r → Crbxyz) → ∀x∀y∀z∀b∀r(x=b → Cbrxyz) is valid.
Now its clear that we need something to connect
Crbxyz and Cbrxyz. But obviously this Crbxyz here:
C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
Has this property:
∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz)
A formal proof might be quite long. We humans on
the other hand somehow see this "obviously" in kind
of a holistic fashion through our visual pattern matching.
Our visual pattern matching seems to be quite
good what concerns commutativity and associativity.
LMAO!
only based on alpha-conversion of bounded quantifers:
∀x∀y∀z∀r∀b(x=r → Crbxyz) → ∀x∀y∀z∀b∀r(x=b → Cbrxyz) is valid.
Now its clear that we need something to connect
Crbxyz and Cbrxyz. But obviously this Crbxyz here:
C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz)
the other hand somehow see this "obviously" in kind
of a holistic fashion through our visual pattern matching.
Our visual pattern matching seems to be quite
good what concerns commutativity and associativity.
LMAO!
Dan Christensen
Nov 23, 2022, 5:06:00 PM11/23/22
to
Dan
Mostowski Collapse
Nov 23, 2022, 5:30:52 PM11/23/22
to
Well it does, just use:
C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
Do you want to spell it letter by letter for you?
Ok here exclusively for our Dumbo aka Wonky Man:
C(red, blue,x,y,z) <=> : Defintion of C predicate
(x=red & y=red & z=red) v (x=blue & y=blue & z=blue): All 3 objects are red or all 3 objects are blue
=> ((x=red & y=red) v (x=blue & y=blue): The two objects x,y are all red or blue
(y=red & z=red) v (y=blue & z=blue) v: The two objects y,z are all red or blue
(x=red & z=red) v (x=blue & z=blue)): The two objects x,z are all red or blue
In summary the Predicate C states:
"If three objects are each painted either red or blue,
then there must be at least two objects of the same color."
C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
Ok here exclusively for our Dumbo aka Wonky Man:
C(red, blue,x,y,z) <=> : Defintion of C predicate
(x=red & y=red & z=red) v (x=blue & y=blue & z=blue): All 3 objects are red or all 3 objects are blue
=> ((x=red & y=red) v (x=blue & y=blue): The two objects x,y are all red or blue
(y=red & z=red) v (y=blue & z=blue) v: The two objects y,z are all red or blue
(x=red & z=red) v (x=blue & z=blue)): The two objects x,z are all red or blue
In summary the Predicate C states:
"If three objects are each painted either red or blue,
then there must be at least two objects of the same color."
Mostowski Collapse
Nov 23, 2022, 5:33:46 PM11/23/22
to
You can also use another reading of "each",
like for example:
C2(red, blue,x,y,z) <=> ((x=red v x=blue) v (y=red v y=blue) & (z=red v z=blue)
∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz)
like for example:
C2(red, blue,x,y,z) <=> ((x=red v x=blue) v (y=red v y=blue) & (z=red v z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
C2 also "obvisouly" satisfies:
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz)
Mostowski Collapse
Nov 23, 2022, 5:35:28 PM11/23/22
to
Typo:
C2(red, blue,x,y,z) <=> ((x=red v x=blue) & (y=red v y=blue) & (z=red v z=blue)
∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz)
C2(red, blue,x,y,z) <=> ((x=red v x=blue) & (y=red v y=blue) & (z=red v z=blue)
=> ((x=red & y=red) v (x=blue & y=blue) v
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
C2 also "obviously" satisfies:
(y=red & z=red) v (y=blue & z=blue) v
(x=red & z=red) v (x=blue & z=blue)))
∀x∀y∀z∀r∀b(Crbxyz → Cbrxyz)
Dan Christensen
Nov 23, 2022, 5:51:51 PM11/23/22
to
> Well it does, just use:
> C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
> => ((x=red & y=red) v (x=blue & y=blue) v
> (y=red & z=red) v (y=blue & z=blue) v
> (x=red & z=red) v (x=blue & z=blue)))
> Do you want to spell it letter by letter for you?
>
[snip]
> C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
> => ((x=red & y=red) v (x=blue & y=blue) v
> (y=red & z=red) v (y=blue & z=blue) v
> (x=red & z=red) v (x=blue & z=blue)))
> Do you want to spell it letter by letter for you?
>
Yes. Just your first 3 lines for now in DC Proof format. By the time you finish that, I think even you will appreciate the difficulties and give up. It certainly won't be any simpler or easier than just working out the 2nd case as I have already done.
Fritz Feldhase
Nov 24, 2022, 2:07:06 AM11/24/22
to
On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> Here I formally prove the following theorem from Wikipedia:
>
> Here I formally prove the following theorem from Wikipedia:
>
> "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
>
>
> Wikipeda provides the following INFORMAL proof:
>
> "A proof: Assume, without loss of generality, that the first object is red.
What an idiotic "proof" (not your fault Dan). We can't just assume that. [Well, technically we can, but...]
>
> "A proof: Assume, without loss of generality, that the first object is red.
Actually, we might consider 2 cases:
1. Assume that non of the objects is red. Then, since "each [of the objects is] painted either red or blue" all objects are blue. But that means that "at least two objects [are] of the same color." So for this case we have proved "the claim".
2. Assume that at least one of the objects is red.
NOW we might proceed: "Assume, without loss of generality, that _the first_ object is red." etc.
Cont.: "If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
> https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
Again this proof is nonsense. What the hell is "the first" object if there are just three object without an order defined on them? Huh?!
It's just the other way round, since there is at least one red object we may just pick one of theses red objects and call it "the first object". etc. THEN we can proceed: "If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
A typical nonsense Wikipedia entry.
Fritz Feldhase
Nov 24, 2022, 2:16:47 AM11/24/22
to
On Thursday, November 24, 2022 at 8:07:06 AM UTC+1, Fritz Feldhase wrote:
> On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> >
> > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
AM(card(M) = 3 & Am(m e M -> red(m) | blue(m)) -> card({m e M : red(m)} >= 2 v card({m e M : blue(m)} >= 2).
> On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> >
> > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
Actually, seems to be an application of the pigeonhole principle to me.
"In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. For example, if one has three gloves (and none is ambidextrous/reversible), then there must be at least two right-handed gloves, or at least two left-handed gloves, because there are three objects, but only two categories of handedness to put them into."
https://en.wikipedia.org/wiki/Pigeonhole_principle
Archimedes Plutonium
Nov 24, 2022, 2:20:47 AM11/24/22
to
>Dan Christensen🤡 Math and Donna Strickland🃏 of Physics "Court Jester of Math"
On Friday, August 6, 2021 at 12:40:30 AM UTC-5, Michael Moroney (Kibo Parry M) wrote:
> fails at math and science:
Kibo Parry M. why is Dan Christensen a blithering idiot of logic with his 2 OR 1 = 3 with AND as subtraction???
Clearly he is insane in logic, but does he need a straightjacket?? And which is a sore for most insanity-- not able to see a slant cut of cone is Oval never the ellipse, or the mindless idiot with his 2 OR 1 = 3 with AND as subtraction because Boole screwed up his AND with OR. And yet Canada lets this loser insane Dan post day after day his trademark insanity.
Ruth Charney, Ken Ribet, Andrew Wiles, Terence Tao, Thomas Hales, John Stillwell, Jill Pipher, Ruth Charney, Ken Ribet, Andrew Beal, John Baez, Roger Penrose, Gerald Edgar, AMS, no-one there can do a Geometry Proof of Fundamental Theorem of Calculus, all they can offer is a limit analysis, so shoddy in logic they never realized that "analyzing" is not the same as "proving" for analyzing is much in the same as "measuring but not proving". And yet, none can do a geometry proof and the reason is quite clear for none can even see that the slant cut in single right-circular cone is a Oval, never the ellipse. So they could never do a geometry proof of FTC even if they wanted to. For they have no logical geometry brain to begin to do anything geometrical. Is it that Andrew Wiles and Terence Tao cannot understand the slant cut in single cone is an Oval, never the ellipse, or is it the foolish Boole logic they teach of 2 OR 1 = 3 with AND as subtraction? Not having a Logical brain to do math, for any rational person would be upset by Wiles, Tao saying truth table of AND is TFFF when it actually is TTTF. Is that why neither Terence Tao or Andrew Wiles can do a geometry proof Fundamental Theorem of Calculus?
Maybe they need to take up Earle Jones offer to wash dishes or pots at Stanford Univ or where ever, for they sure cannot do mathematics.
Why are these people failures of Math?? For none can even contemplate these 4 questions.
1) think a slant cut in single cone is a ellipse when it is proven to be a Oval, never the ellipse. For the cone and oval have 1 axis of symmetry, while ellipse has 2.
2) think Boole logic is correct with AND truth table being TFFF when it really is TTTF in order to avoid 2 OR 1 =3 with AND as subtraction
3) can never do a geometry proof of Fundamental Theorem of Calculus and are too ignorant in math to understand that analysis of something is not proving something in their "limit hornswaggle"
4) too stupid in science to ask the question of physics-- is the 1897 Thomson discovery of a 0.5MeV particle actually the Dirac magnetic monopole and that the muon is the true electron of atoms stuck inside a 840MeV proton torus doing the Faraday law. Showing that Peter Higgs, Sheldon Glashow, Ed Witten, John Baez, Roger Penrose, Arthur B. McDonald are sapheads when it comes to logical thinking in physics with their do nothing proton, do nothing electron.
Is Jim Holt, Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
John Venn, William Gustason, Richmond H. Thomason, more of propagandists and belong in "Abnormal Psychology" dept than in the department of logic, like Dan Christensen a laugh a minute logician? Probably because none can admit slant cut in single cone is a Oval, never the ellipse, due to axes of symmetry for cone and oval have 1 while ellipse has 2. Why they cannot even count beyond 1. Yet their minds were never good enough to see the error nor admit to their mistakes. They failed logic so badly they accept Boole's insane AND truth table of TFFF when it is TTTF avoiding the painful 2 OR 1 = 3 with AND as subtraction. Or is it because none of these logicians has a single marble of logic in their entire brain to realize calculus requires a geometry proof of Fundamental Theorem of Calculus, not a "limit analysis" for analysis is like a measurement, not a proving exercise. Analysis does not prove, only adds data and facts, but never is a proof of itself. I analyze things daily, and none of which is a proof. So are all these logicians like what Clutterfreak the propaganda stooge says they are.
> On Friday, July 2, 2021 at 9:47:42 AM UTC-5, Dan Christensen wrote:
> > You may be giving him too much credit here. Judging by his bizarre antics here, he has given up obtaining any kind of positive recognition.
> >
> > Dan
>
> Partial List of the World's Crackpot Logicians-- should be in a college Abnormal-Psychology department, not Logic//
>
> Peter Bruce Andrews, Lennart Aqvist, Henk Barendregt, John Lane Bell, Nuel Belnap,
> Paul Benacerraf, Jean Paul Van Bendegem, Johan van Benthem, Jean-Yves Beziau,
> Andrea Bonomi, Nicolas Bourbaki (a group of logic fumblers), Alan Richard Bundy, Gregory Chaitin,
> Jack Copeland, John Corcoran, Dirk van Dalen, Martin Davis, Michael A.E. Dummett, John Etchemendy, Hartry Field, Kit Fine, Melvin Fitting, Matthew Foreman, Michael Fourman,
> Harvey Friedman, Dov Gabbay, L.T.F. Gamut (group of logic fumblers), Sol Garfunkel, Jean-Yves Girard, Siegfried Gottwald, Jeroen Groenendijk, Susan Haack, Leo Harrington, William Alvin Howard,
> Ronald Jensen, Dick de Jongh, David Kaplan, Alexander S. Kechris, Howard Jerome Keisler,
> Robert Kowalski, Georg Kreisel, Saul Kripke, Kenneth Kunen, Karel Lambert, Penelope Maddy,
> David Makinson, Isaac Malitz, Gary R. Mar, Donald A. Martin, Per Martin-Lof,Yiannis N. Moschovakis, Jeff Paris, Charles Parsons, Solomon Passy, Lorenzo Pena, Dag Prawitz,
> Graham Priest, Michael O. Rabin, Gerald Sacks, Dana Scott, Stewart Shapiro, Theodore Slaman,
> Robert M. Solovay, John R. Steel, Martin Stokhof, Anne Sjerp Troelstra, Alasdair Urquhart,
> Moshe Y. Vardi, W. Hugh Woodin, John Woods
>
> Now I should include the authors of Logic textbooks for they, more than most, perpetuate and crank the error filled logic, the Horrible Error of 2 OR 1 = 3 with 2 AND 1 = 1, that is forced down the throats of young students, making them cripples of ever thinking straight and clearly.
>
> Many of these authors have passed away but their error filled books are a scourge to modern education
>
> George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap,
> Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi, Michael Withey,
> Patrick Hurley, Harry J Gensler, David Kelley, Jesse Bollinger, Theodore Sider,
> David Barker-Plummer, I. C. Robledo, John Nolt, Peter Smith, Stan Baronett, Jim Holt,
> Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
> John Venn, William Gustason, Richmond H. Thomason,
> > #5-1, 134th published book
> >
> > > > > Introduction to TEACHING TRUE MATHEMATICS: Volume 1 for ages 5 through 26, math textbook series, book 1 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > The 134th book of AP, and belatedly late, for I had already written the series of TEACHING TRUE MATHEMATICS in a 7 volume, 8 book set. This would be the first book in that 8 book set (one of the books is a companion book to 1st year college). But I suppose that I needed to write the full series before I could write the Introduction and know what I had to talk about and talk about in a logical progression order. Sounds paradoxical in a sense, that I needed to write the full series first and then go back and write the Introduction. But in another sense, hard to write an introduction on something you have not really fully done and completed. For example to know what is error filled Old Math and to list those errors in a logical order requires me to write the full 7 volumes in order to list in order the mistakes.
> >
> > Cover Picture: Mathematics begins with counting, with numbers, with quantity. But counting numbers needs geometry for something to count in the first place. So here in this picture of the generalized Hydrogen atom of chemistry and physics is a torus geometry of 8 rings of a proton torus and one ring where my fingers are, is a equator ring that is the muon and thrusting through the proton torus at the equator of the torus. So we count 9 rings in all. So math is created by atoms and math numbers exist because atoms have many geometry figures to count. And geometry exists because atoms have shapes and different figures.
> >
> > Product details
> > • ASIN : B08K2XQB4M
> > • Publication date : September 24, 2020
> > • Language : English
> > • File size : 576 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 23 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #224,974 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3 in 45-Minute Science & Math Short Reads
> > ◦ #23 in Calculus (Kindle Store)
> > ◦ #182 in Calculus (Books)
> >
> >
> >
> > #5-2, 45th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> >
> >
> >
> > #1 New Releasein General Geometry
> >
> >
> > Last revision was 2NOV2020. And this is AP's 45th published book of science.
> > Preface: Volume 2 takes the 5 year old student through to senior in High School for their math education.
> >
> > This is a textbook series in several volumes that carries every person through all his/her math education starting age 5 up to age 26. Volume 2 is for age 5 year old to that of senior in High School, that is needed to do both science and math. Every other math book is incidental to this series of Teaching True Mathematics.
> >
> > It is a journal-textbook because Amazon's Kindle offers me the ability to edit overnight, and to change the text, almost on a daily basis. A unique first in education textbooks-- almost a continual overnight editing. Adding new text, correcting text. Volume 2 takes the 5 year old student through to senior in High School for their math education. Volume 3 carries the Freshperson in College for their math calculus education.
> >
> > Cover Picture: The Numbers as Integers from 0 to 100, and 10 Grid when dividing by 10, and part of the 100 Grid when dividing by 100. Decimal Grid Numbers are the true numbers of mathematics. The Reals, the rationals & irrationals, the algebraic & transcendentals, the imaginary & Complex, and the negative-numbers are all fake numbers. For, to be a true number, you have to "be counted" by mathematical induction. The smallest Grid system is the Decimal 10 Grid.
> >
> > Length: 399 pages
> >
> >
> >
> >
> > Product details
> > ASIN : B07RG7BVZW
> > Publication date : May 2, 2019
> > Language : English
> > File size : 2023 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 399 pages
> > Lending : Enabled
> > Best Sellers Rank: #235,426 in Kindle Store (See Top 100 in Kindle Store)
> > #15 in General Geometry
> > #223 in Geometry & Topology (Books)
> >
> >
> >
> >
> > #5-3, 55th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 3 for age 18-19, 1st year College Calculus, math textbook series, book 3 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 25Jun2021. And this is AP's 55th published book of science.
> >
> > Teaching True Mathematics, by Archimedes Plutonium 2019
> >
> > Preface: This is volume 3, book 3 of Teaching True Mathematics, designed for College Freshperson students, 1st year college students of age 18-19. It is the continuation of volume 2 for ages 5 through 18 years old.
> >
> > The main major topic is the AP-EM equations of electricity and magnetism, the mathematics for the laws of electricity and magnetism; what used to be called the Maxwell Equations of Physics. The 1st Year College Math has to prepare all students with the math for all the sciences. So 1st year college Math is like a huge intersection station that has to prepare students with the math they need to do the hard sciences such as physics, chemistry, biology, astronomy, geology, etc. What this means is, 1st year college is calculus that allows the student to work with electricity and magnetism. All the math that is needed to enable students to do electricity and magnetism. In Old Math before this textbook, those Old Math textbooks would end in 1/3 of the text about Arclength, vector space, div, curl, Line Integral, Green's, Stokes, Divergence theorem trying to reach and be able to teach Maxwell Equations. But sadly, barely any Old Math classroom reached that 1/3 ending of the textbook, and left all those college students without any math to tackle electricity and magnetism. And most of Old Math was just muddle headed wrong even if they covered the last 1/3 of the textbook. And that is totally unacceptable in science. This textbook fixes that huge hole and gap in Old Math education.
> >
> > And there is no way around it, that a course in 1st year College Calculus is going to do a lot of hands on experiment with electricity and magnetism, and is required of the students to buy a list of physics apparatus-- multimeter, galvanometer, coil, bar magnet, alligator clip wires, electromagnet, iron filing case, and possibly even a 12 volt transformer, all shown in the cover picture. The beginning of this textbook and the middle section all leads into the ending of this textbook-- we learn the AP-EM Equations and how to use those equations. And there is no escaping the fact that it has to be hands on physics experiments in the classroom of mathematics.
> >
> > But, do not be scared, for this is all easy easy easy. For if you passed and enjoyed Volume 2 TEACHING TRUE MATHEMATICS, then I promise you, you will not be stressed with Volume 3, for I go out of my way to make it clear and understandable.
> >
> > Warning: this is a Journal Textbook, meaning that I am constantly adding new material, constantly revising, constantly fixing mistakes or making things more clear. So if you read this book in August of 2019, chances are it is different when you read it in September 2019. Ebooks allow authors the freedom to improve their textbooks on a ongoing basis.
> >
> > The 1st year college math should be about the math that prepares any and all students for science, whether they branch out into physics, chemistry, biology, geology, astronomy, or math, they should have all the math in 1st year college that will carry them through those science studies. I make every attempt possible to make math easy to understand, easy to learn and hopefully fun.
> >
> > Product details
> > • ASIN : B07WN9RVXD
> > • Publication date : August 16, 2019
> > • Language : English
> > • File size : 1390 KB
> > • Simultaneous device usage : Unlimited
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 236 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #1,377,070 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #411 in Calculus (Kindle Store)
> > ◦ #2,480 in Calculus (Books)
> >
> >
> >
> >
> > #5-4, 56th published book
> >
> > COLLEGE CALCULUS GUIDE to help students recognize math professor spam from math truth & reality// math textbook series, book 4 Kindle Edition
> >
> > by Archimedes Plutonium (Author)
> >
> >
> > #1 New Releasein 15-Minute Science & Math Short Reads
> >
> >
> > This textbook is the companion guide book to AP's Teaching True Mathematics, 1st year College. It is realized that Old Math will take a long time in removing their fake math, so in the interim period, this Guide book is designed to speed up the process of removing fake Calculus out of the education system, the fewer students we punish with forcing them with fake Calculus, the better we are.
> > Cover Picture: This book is part comedy, for when you cannot reason with math professors that they have many errors to fix, that 90% of their Calculus is in error, you end up resorting to comedy, making fun of them, to prod them to fix their errors. To prod them to "do right by the students of the world" not their entrenched propaganda.
> > Length: 54 pages
> >
> >
> > Product details
> > File Size: 1035 KB
> > Print Length: 64 pages
> > Simultaneous Device Usage: Unlimited
> > Publication Date: August 18, 2019
> > Sold by: Amazon.com Services LLC
> > Language: English
> > ASIN: B07WNGLQ85
> > Text-to-Speech: Enabled
> > X-Ray: Not Enabled
> > Word Wise: Not Enabled
> > Lending: Enabled
> > Enhanced Typesetting: Enabled
> > Amazon Best Sellers Rank: #253,425 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
> > #38 in 90-Minute Science & Math Short Reads
> > #318 in Calculus (Books)
> > #48 in Calculus (Kindle Store)
> >
> > #5-5, 72nd published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 4 for age 19-20 Sophomore-year College, math textbook series, book 5 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Preface: This is volume 4, book 5 of Teaching True Mathematics, designed for College Sophomore-year students, students of age 19-20. It is the continuation of volume 3 in the end-goal of learning how to do the mathematics of electricity and magnetism, because everything in physics is nothing but atoms and atoms are nothing but electricity and magnetism. To know math, you have to know physics. We learned the Calculus of 2nd dimension and applied it to the equations of physics for electricity and magnetism. But we did not learn the calculus of those equations for 3rd dimension. So, you can say that Sophomore year College math is devoted to 3D Calculus. This sophomore year college we fill in all the calculus, and we start over on all of Geometry, for geometry needs a modern day revision. And pardon me for this book is mostly reading, and the students doing less calculations. The classroom of this textbook has the teacher go through page by page to get the students comprehending and understanding of what is being taught. There are many hands on experiments also.
> >
> > Cover Picture shows some toruses, some round some square, torus of rings, thin strips of rings or squares and shows them laid flat. That is Calculus of 3rd dimension that lays a ring in a torus to be flat in 2nd dimension.
> > Length: 105 pages
> >
> > Product details
> > • ASIN : B0828M34VL
> > • Publication date : December 2, 2019
> > • Language : English
> > • File size : 952 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 105 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #242,037 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #36 in Calculus (Kindle Store)
> > ◦ #219 in Calculus (Books)
> >
> >
> > #5-6, 75th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 5 for age 20-21 Junior-year of College, math textbook series, book 6 Kindle Edition
> > by Archimedes Plutonium 2019
> >
> > This is volume 5, book 6 of Teaching True Mathematics, designed for College Junior-year students, students of age 20-21. In first year college Calculus we learned calculus of the 2nd dimension and applied it to the equations of physics for electricity and magnetism. And in sophomore year we learned calculus of 3rd dimension to complete our study of the mathematics needed to do the physics of electricity and magnetism. Now, junior year college, we move onto something different, for we focus mostly on logic now and especially the logic of what is called the "mathematical proof". Much of what the student has learned about mathematics so far has been given to her or him as stated knowledge, accept it as true because I say so. But now we are going to do math proofs. Oh, yes, we did prove a few items here and there, such as why the Decimal Grid Number system is so special, such as the Pythagorean Theorem, such as the Fundamental Theorem of Calculus with its right-triangle hinged up or down. But many ideas we did not prove, we just stated them and expected all students to believe them true. And you are now juniors in college and we are going to start to prove many of those ideas and teach you "what is a math proof". Personally, I myself feel that the math proof is overrated, over hyped. But the math proof is important for one reason-- it makes you better scientists of knowing what is true and what is a shaky idea. A math proof is the same as "thinking straight and thinking clearly". And all scientists need to think straight and think clearly. But before we get to the Mathematics Proof, we have to do Probability and Statistics. What you learned in Grade School, then High School, then College, called Sigma Error, now becomes Probability and Statistics. It is important because all sciences including mathematics needs and uses Probability and Statistics. So, our job for junior-year of college mathematics is all cut out and ahead for us, no time to waste, let us get going.
> >
> > Cover Picture: is a sample of the Array Proof, a proof the ellipse is not a conic but rather a cylinder cut wherein the oval is the slant cut of a cone, not the ellipse.
> >
> > Length: 175 pages
> >
> >
> > Product details
> > ASIN : B0836F1YF6
> > Publication date : December 26, 2019
> > Language : English
> > File size : 741 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 175 pages
> > Lending : Enabled
> > Best Sellers Rank: #3,768,255 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3,591 in Probability & Statistics (Kindle Store)
> > ◦ #19,091 in Probability & Statistics (Books)
> >
> >
> >
> > #5-7, 89th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 6 for age 21-22 Senior-year of College, math textbook series, book 7 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revision was 6Feb2021.
> > Preface: This is the last year of College for mathematics and we have to mostly summarize all of mathematics as best we can. And set a new pattern to prepare students going on to math graduate school. A new pattern of work habits, because graduate school is more of research and explore on your own. So in this final year, I am going to eliminate tests, and have it mostly done as homework assignments.
> >
> > Cover Picture: Again and again, many times in math, the mind is not good enough alone to think straight and clear, and you need tools to hands-on see how it works. Here is a collection of tools for this senior year college classes. There is a pencil, clipboard, graph paper, compass, divider, protractor, slide-ruler. And for this year we spend a lot of time on the parallelepiped, showing my wood model, and showing my erector set model held together by wire loops in the corners. The plastic square is there only to hold up the erector set model.
> >
> > Length: 110 pages
> >
> > Product details
> > ASIN : B084V11BGY
> > Publication date : February 15, 2020
> > Language : English
> > File size : 826 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Enabled
> > Print length : 110 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,965 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #345 in Mathematics (Kindle Store)
> > ◦ #373 in Physics (Kindle Store)
> > ◦ #2,256 in Physics (Books)
> >
> > #5-8, 90th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 7 for age 22-26 Graduate school, math textbook series, book 8 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revised 1NOV2020. This was AP's 90th published book of science.
> >
> > Preface: This is College Graduate School mathematics. Congratulations, you made it this far. To me, graduate school is mostly research, research mathematics and that means also physics. So it is going to be difficult to do math without physics. Of course, we focus on the mathematics of these research projects.
> >
> > My textbook for Graduate school is just a template and the professors teaching the graduate students are free of course to follow their own projects, but in terms of being physics and math combined. What I list below is a template for possible projects.
> >
> > So, in the below projects, I list 36 possible research projects that a graduate student my like to undertake, or partake. I list those 36 projects with a set of parentheses like this (1), (2), (3), etc. Not to be confused with the chapters listing as 1), 2), 3), etc. I list 36 projects but the professor can offer his/her own list, and I expect students with their professor, to pick a project and to monitor the student as to his/her progresses through the research. I have listed each project then cited some of my own research into these projects, below each project is an entry. Those entries are just a help or helper in getting started or acquainted with the project. The entry has a date time group and a newsgroup that I posted to such as sci.math or plutonium-atom-universe Google newsgroups. Again the entry is just a help or helper in getting started.
> >
> > Now instead of picking one or two projects for your Graduate years of study, some may select all 36 projects where you write a short paper on each project. Some may be bored with just one or two projects and opt for all 36.
> >
> > Cover Picture: A photo by my iphone of a page on Permutations of the Jacobs book Mathematics: A Human Endeavor, 1970. One of the best textbooks ever written in Old Math, not for its contents because there are many errors, but for its teaching style. It is extremely rare to find a math textbook written for the student to learn. Probably because math professors rarely learned how to teach in the first place; only learned how to unintentionally obfuscate. The page I photographed is important because it is the interface between geometry's perimeter or surface area versus geometry's area or volume, respectively. Or, an interface of pure numbers with that of geometry. But I have more to say on this below.
> > Length: 296 pages
> >
> > Product details
> > ASIN : B085DF8R7V
> > Publication date : March 1, 2020
> > Language : English
> > File size : 828 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 296 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,981 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #13 in General Geometry
> > ◦ #213 in Geometry & Topology (Books)
> >
> >
> >
> > #5-8, 160th published book
> >
> > MATHOPEDIA-- List of 80 fakes and mistakes of Old Math// Student teaches professor Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 28Apr2022. And this is AP's 160th book of Science.
> > Preface:
> > A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.
> > The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.
> > The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery. I know because I have been there.
> > Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.
> > I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).
> >
> > Product details
> > • ASIN : B09MZTLRL5
> > • Publication date : December 2, 2021
> > • Language : English
> > • File size : 1149 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 65 pages
> > • Lending : Enabled
On Friday, August 6, 2021 at 12:40:30 AM UTC-5, Michael Moroney (Kibo Parry M) wrote:
> fails at math and science:
Kibo Parry M. why is Dan Christensen a blithering idiot of logic with his 2 OR 1 = 3 with AND as subtraction???
Clearly he is insane in logic, but does he need a straightjacket?? And which is a sore for most insanity-- not able to see a slant cut of cone is Oval never the ellipse, or the mindless idiot with his 2 OR 1 = 3 with AND as subtraction because Boole screwed up his AND with OR. And yet Canada lets this loser insane Dan post day after day his trademark insanity.
Ruth Charney, Ken Ribet, Andrew Wiles, Terence Tao, Thomas Hales, John Stillwell, Jill Pipher, Ruth Charney, Ken Ribet, Andrew Beal, John Baez, Roger Penrose, Gerald Edgar, AMS, no-one there can do a Geometry Proof of Fundamental Theorem of Calculus, all they can offer is a limit analysis, so shoddy in logic they never realized that "analyzing" is not the same as "proving" for analyzing is much in the same as "measuring but not proving". And yet, none can do a geometry proof and the reason is quite clear for none can even see that the slant cut in single right-circular cone is a Oval, never the ellipse. So they could never do a geometry proof of FTC even if they wanted to. For they have no logical geometry brain to begin to do anything geometrical. Is it that Andrew Wiles and Terence Tao cannot understand the slant cut in single cone is an Oval, never the ellipse, or is it the foolish Boole logic they teach of 2 OR 1 = 3 with AND as subtraction? Not having a Logical brain to do math, for any rational person would be upset by Wiles, Tao saying truth table of AND is TFFF when it actually is TTTF. Is that why neither Terence Tao or Andrew Wiles can do a geometry proof Fundamental Theorem of Calculus?
Maybe they need to take up Earle Jones offer to wash dishes or pots at Stanford Univ or where ever, for they sure cannot do mathematics.
Why are these people failures of Math?? For none can even contemplate these 4 questions.
1) think a slant cut in single cone is a ellipse when it is proven to be a Oval, never the ellipse. For the cone and oval have 1 axis of symmetry, while ellipse has 2.
2) think Boole logic is correct with AND truth table being TFFF when it really is TTTF in order to avoid 2 OR 1 =3 with AND as subtraction
3) can never do a geometry proof of Fundamental Theorem of Calculus and are too ignorant in math to understand that analysis of something is not proving something in their "limit hornswaggle"
4) too stupid in science to ask the question of physics-- is the 1897 Thomson discovery of a 0.5MeV particle actually the Dirac magnetic monopole and that the muon is the true electron of atoms stuck inside a 840MeV proton torus doing the Faraday law. Showing that Peter Higgs, Sheldon Glashow, Ed Witten, John Baez, Roger Penrose, Arthur B. McDonald are sapheads when it comes to logical thinking in physics with their do nothing proton, do nothing electron.
Is Jim Holt, Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
John Venn, William Gustason, Richmond H. Thomason, more of propagandists and belong in "Abnormal Psychology" dept than in the department of logic, like Dan Christensen a laugh a minute logician? Probably because none can admit slant cut in single cone is a Oval, never the ellipse, due to axes of symmetry for cone and oval have 1 while ellipse has 2. Why they cannot even count beyond 1. Yet their minds were never good enough to see the error nor admit to their mistakes. They failed logic so badly they accept Boole's insane AND truth table of TFFF when it is TTTF avoiding the painful 2 OR 1 = 3 with AND as subtraction. Or is it because none of these logicians has a single marble of logic in their entire brain to realize calculus requires a geometry proof of Fundamental Theorem of Calculus, not a "limit analysis" for analysis is like a measurement, not a proving exercise. Analysis does not prove, only adds data and facts, but never is a proof of itself. I analyze things daily, and none of which is a proof. So are all these logicians like what Clutterfreak the propaganda stooge says they are.
> On Friday, July 2, 2021 at 9:47:42 AM UTC-5, Dan Christensen wrote:
> > You may be giving him too much credit here. Judging by his bizarre antics here, he has given up obtaining any kind of positive recognition.
> >
> > Dan
>
> Partial List of the World's Crackpot Logicians-- should be in a college Abnormal-Psychology department, not Logic//
>
> Peter Bruce Andrews, Lennart Aqvist, Henk Barendregt, John Lane Bell, Nuel Belnap,
> Paul Benacerraf, Jean Paul Van Bendegem, Johan van Benthem, Jean-Yves Beziau,
> Andrea Bonomi, Nicolas Bourbaki (a group of logic fumblers), Alan Richard Bundy, Gregory Chaitin,
> Jack Copeland, John Corcoran, Dirk van Dalen, Martin Davis, Michael A.E. Dummett, John Etchemendy, Hartry Field, Kit Fine, Melvin Fitting, Matthew Foreman, Michael Fourman,
> Harvey Friedman, Dov Gabbay, L.T.F. Gamut (group of logic fumblers), Sol Garfunkel, Jean-Yves Girard, Siegfried Gottwald, Jeroen Groenendijk, Susan Haack, Leo Harrington, William Alvin Howard,
> Ronald Jensen, Dick de Jongh, David Kaplan, Alexander S. Kechris, Howard Jerome Keisler,
> Robert Kowalski, Georg Kreisel, Saul Kripke, Kenneth Kunen, Karel Lambert, Penelope Maddy,
> David Makinson, Isaac Malitz, Gary R. Mar, Donald A. Martin, Per Martin-Lof,Yiannis N. Moschovakis, Jeff Paris, Charles Parsons, Solomon Passy, Lorenzo Pena, Dag Prawitz,
> Graham Priest, Michael O. Rabin, Gerald Sacks, Dana Scott, Stewart Shapiro, Theodore Slaman,
> Robert M. Solovay, John R. Steel, Martin Stokhof, Anne Sjerp Troelstra, Alasdair Urquhart,
> Moshe Y. Vardi, W. Hugh Woodin, John Woods
>
> Now I should include the authors of Logic textbooks for they, more than most, perpetuate and crank the error filled logic, the Horrible Error of 2 OR 1 = 3 with 2 AND 1 = 1, that is forced down the throats of young students, making them cripples of ever thinking straight and clearly.
>
> Many of these authors have passed away but their error filled books are a scourge to modern education
>
> George Boole, William Jevons, Bertrand Russell, Kurt Godel, Rudolf Carnap,
> Ludwig Wittgenstein, Willard Quine, Alfred North Whitehead, Irving Copi, Michael Withey,
> Patrick Hurley, Harry J Gensler, David Kelley, Jesse Bollinger, Theodore Sider,
> David Barker-Plummer, I. C. Robledo, John Nolt, Peter Smith, Stan Baronett, Jim Holt,
> Virginia Klenk, David Agler, Susanne K. Langer, Gary M. Hardegree, Raymond M. Smullyan,
> John Venn, William Gustason, Richmond H. Thomason,
> > #5-1, 134th published book
> >
> > > > > Introduction to TEACHING TRUE MATHEMATICS: Volume 1 for ages 5 through 26, math textbook series, book 1 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > The 134th book of AP, and belatedly late, for I had already written the series of TEACHING TRUE MATHEMATICS in a 7 volume, 8 book set. This would be the first book in that 8 book set (one of the books is a companion book to 1st year college). But I suppose that I needed to write the full series before I could write the Introduction and know what I had to talk about and talk about in a logical progression order. Sounds paradoxical in a sense, that I needed to write the full series first and then go back and write the Introduction. But in another sense, hard to write an introduction on something you have not really fully done and completed. For example to know what is error filled Old Math and to list those errors in a logical order requires me to write the full 7 volumes in order to list in order the mistakes.
> >
> > Cover Picture: Mathematics begins with counting, with numbers, with quantity. But counting numbers needs geometry for something to count in the first place. So here in this picture of the generalized Hydrogen atom of chemistry and physics is a torus geometry of 8 rings of a proton torus and one ring where my fingers are, is a equator ring that is the muon and thrusting through the proton torus at the equator of the torus. So we count 9 rings in all. So math is created by atoms and math numbers exist because atoms have many geometry figures to count. And geometry exists because atoms have shapes and different figures.
> >
> > Product details
> > • ASIN : B08K2XQB4M
> > • Publication date : September 24, 2020
> > • Language : English
> > • File size : 576 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 23 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #224,974 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3 in 45-Minute Science & Math Short Reads
> > ◦ #23 in Calculus (Kindle Store)
> > ◦ #182 in Calculus (Books)
> >
> >
> >
> > #5-2, 45th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 2 for ages 5 to 18, math textbook series, book 2 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> >
> >
> >
> > #1 New Releasein General Geometry
> >
> >
> > Last revision was 2NOV2020. And this is AP's 45th published book of science.
> > Preface: Volume 2 takes the 5 year old student through to senior in High School for their math education.
> >
> > This is a textbook series in several volumes that carries every person through all his/her math education starting age 5 up to age 26. Volume 2 is for age 5 year old to that of senior in High School, that is needed to do both science and math. Every other math book is incidental to this series of Teaching True Mathematics.
> >
> > It is a journal-textbook because Amazon's Kindle offers me the ability to edit overnight, and to change the text, almost on a daily basis. A unique first in education textbooks-- almost a continual overnight editing. Adding new text, correcting text. Volume 2 takes the 5 year old student through to senior in High School for their math education. Volume 3 carries the Freshperson in College for their math calculus education.
> >
> > Cover Picture: The Numbers as Integers from 0 to 100, and 10 Grid when dividing by 10, and part of the 100 Grid when dividing by 100. Decimal Grid Numbers are the true numbers of mathematics. The Reals, the rationals & irrationals, the algebraic & transcendentals, the imaginary & Complex, and the negative-numbers are all fake numbers. For, to be a true number, you have to "be counted" by mathematical induction. The smallest Grid system is the Decimal 10 Grid.
> >
> > Length: 399 pages
> >
> >
> >
> >
> > Product details
> > ASIN : B07RG7BVZW
> > Publication date : May 2, 2019
> > Language : English
> > File size : 2023 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 399 pages
> > Lending : Enabled
> > Best Sellers Rank: #235,426 in Kindle Store (See Top 100 in Kindle Store)
> > #15 in General Geometry
> > #223 in Geometry & Topology (Books)
> >
> >
> >
> >
> > #5-3, 55th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 3 for age 18-19, 1st year College Calculus, math textbook series, book 3 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 25Jun2021. And this is AP's 55th published book of science.
> >
> > Teaching True Mathematics, by Archimedes Plutonium 2019
> >
> > Preface: This is volume 3, book 3 of Teaching True Mathematics, designed for College Freshperson students, 1st year college students of age 18-19. It is the continuation of volume 2 for ages 5 through 18 years old.
> >
> > The main major topic is the AP-EM equations of electricity and magnetism, the mathematics for the laws of electricity and magnetism; what used to be called the Maxwell Equations of Physics. The 1st Year College Math has to prepare all students with the math for all the sciences. So 1st year college Math is like a huge intersection station that has to prepare students with the math they need to do the hard sciences such as physics, chemistry, biology, astronomy, geology, etc. What this means is, 1st year college is calculus that allows the student to work with electricity and magnetism. All the math that is needed to enable students to do electricity and magnetism. In Old Math before this textbook, those Old Math textbooks would end in 1/3 of the text about Arclength, vector space, div, curl, Line Integral, Green's, Stokes, Divergence theorem trying to reach and be able to teach Maxwell Equations. But sadly, barely any Old Math classroom reached that 1/3 ending of the textbook, and left all those college students without any math to tackle electricity and magnetism. And most of Old Math was just muddle headed wrong even if they covered the last 1/3 of the textbook. And that is totally unacceptable in science. This textbook fixes that huge hole and gap in Old Math education.
> >
> > And there is no way around it, that a course in 1st year College Calculus is going to do a lot of hands on experiment with electricity and magnetism, and is required of the students to buy a list of physics apparatus-- multimeter, galvanometer, coil, bar magnet, alligator clip wires, electromagnet, iron filing case, and possibly even a 12 volt transformer, all shown in the cover picture. The beginning of this textbook and the middle section all leads into the ending of this textbook-- we learn the AP-EM Equations and how to use those equations. And there is no escaping the fact that it has to be hands on physics experiments in the classroom of mathematics.
> >
> > But, do not be scared, for this is all easy easy easy. For if you passed and enjoyed Volume 2 TEACHING TRUE MATHEMATICS, then I promise you, you will not be stressed with Volume 3, for I go out of my way to make it clear and understandable.
> >
> > Warning: this is a Journal Textbook, meaning that I am constantly adding new material, constantly revising, constantly fixing mistakes or making things more clear. So if you read this book in August of 2019, chances are it is different when you read it in September 2019. Ebooks allow authors the freedom to improve their textbooks on a ongoing basis.
> >
> > The 1st year college math should be about the math that prepares any and all students for science, whether they branch out into physics, chemistry, biology, geology, astronomy, or math, they should have all the math in 1st year college that will carry them through those science studies. I make every attempt possible to make math easy to understand, easy to learn and hopefully fun.
> >
> > Product details
> > • ASIN : B07WN9RVXD
> > • Publication date : August 16, 2019
> > • Language : English
> > • File size : 1390 KB
> > • Simultaneous device usage : Unlimited
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 236 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #1,377,070 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #411 in Calculus (Kindle Store)
> > ◦ #2,480 in Calculus (Books)
> >
> >
> >
> >
> > #5-4, 56th published book
> >
> > COLLEGE CALCULUS GUIDE to help students recognize math professor spam from math truth & reality// math textbook series, book 4 Kindle Edition
> >
> > by Archimedes Plutonium (Author)
> >
> >
> > #1 New Releasein 15-Minute Science & Math Short Reads
> >
> >
> > This textbook is the companion guide book to AP's Teaching True Mathematics, 1st year College. It is realized that Old Math will take a long time in removing their fake math, so in the interim period, this Guide book is designed to speed up the process of removing fake Calculus out of the education system, the fewer students we punish with forcing them with fake Calculus, the better we are.
> > Cover Picture: This book is part comedy, for when you cannot reason with math professors that they have many errors to fix, that 90% of their Calculus is in error, you end up resorting to comedy, making fun of them, to prod them to fix their errors. To prod them to "do right by the students of the world" not their entrenched propaganda.
> > Length: 54 pages
> >
> >
> > Product details
> > File Size: 1035 KB
> > Print Length: 64 pages
> > Simultaneous Device Usage: Unlimited
> > Publication Date: August 18, 2019
> > Sold by: Amazon.com Services LLC
> > Language: English
> > ASIN: B07WNGLQ85
> > Text-to-Speech: Enabled
> > X-Ray: Not Enabled
> > Word Wise: Not Enabled
> > Lending: Enabled
> > Enhanced Typesetting: Enabled
> > Amazon Best Sellers Rank: #253,425 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
> > #38 in 90-Minute Science & Math Short Reads
> > #318 in Calculus (Books)
> > #48 in Calculus (Kindle Store)
> >
> > #5-5, 72nd published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 4 for age 19-20 Sophomore-year College, math textbook series, book 5 Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Preface: This is volume 4, book 5 of Teaching True Mathematics, designed for College Sophomore-year students, students of age 19-20. It is the continuation of volume 3 in the end-goal of learning how to do the mathematics of electricity and magnetism, because everything in physics is nothing but atoms and atoms are nothing but electricity and magnetism. To know math, you have to know physics. We learned the Calculus of 2nd dimension and applied it to the equations of physics for electricity and magnetism. But we did not learn the calculus of those equations for 3rd dimension. So, you can say that Sophomore year College math is devoted to 3D Calculus. This sophomore year college we fill in all the calculus, and we start over on all of Geometry, for geometry needs a modern day revision. And pardon me for this book is mostly reading, and the students doing less calculations. The classroom of this textbook has the teacher go through page by page to get the students comprehending and understanding of what is being taught. There are many hands on experiments also.
> >
> > Cover Picture shows some toruses, some round some square, torus of rings, thin strips of rings or squares and shows them laid flat. That is Calculus of 3rd dimension that lays a ring in a torus to be flat in 2nd dimension.
> > Length: 105 pages
> >
> > Product details
> > • ASIN : B0828M34VL
> > • Publication date : December 2, 2019
> > • Language : English
> > • File size : 952 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 105 pages
> > • Lending : Enabled
> > • Best Sellers Rank: #242,037 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #36 in Calculus (Kindle Store)
> > ◦ #219 in Calculus (Books)
> >
> >
> > #5-6, 75th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 5 for age 20-21 Junior-year of College, math textbook series, book 6 Kindle Edition
> > by Archimedes Plutonium 2019
> >
> > This is volume 5, book 6 of Teaching True Mathematics, designed for College Junior-year students, students of age 20-21. In first year college Calculus we learned calculus of the 2nd dimension and applied it to the equations of physics for electricity and magnetism. And in sophomore year we learned calculus of 3rd dimension to complete our study of the mathematics needed to do the physics of electricity and magnetism. Now, junior year college, we move onto something different, for we focus mostly on logic now and especially the logic of what is called the "mathematical proof". Much of what the student has learned about mathematics so far has been given to her or him as stated knowledge, accept it as true because I say so. But now we are going to do math proofs. Oh, yes, we did prove a few items here and there, such as why the Decimal Grid Number system is so special, such as the Pythagorean Theorem, such as the Fundamental Theorem of Calculus with its right-triangle hinged up or down. But many ideas we did not prove, we just stated them and expected all students to believe them true. And you are now juniors in college and we are going to start to prove many of those ideas and teach you "what is a math proof". Personally, I myself feel that the math proof is overrated, over hyped. But the math proof is important for one reason-- it makes you better scientists of knowing what is true and what is a shaky idea. A math proof is the same as "thinking straight and thinking clearly". And all scientists need to think straight and think clearly. But before we get to the Mathematics Proof, we have to do Probability and Statistics. What you learned in Grade School, then High School, then College, called Sigma Error, now becomes Probability and Statistics. It is important because all sciences including mathematics needs and uses Probability and Statistics. So, our job for junior-year of college mathematics is all cut out and ahead for us, no time to waste, let us get going.
> >
> > Cover Picture: is a sample of the Array Proof, a proof the ellipse is not a conic but rather a cylinder cut wherein the oval is the slant cut of a cone, not the ellipse.
> >
> > Length: 175 pages
> >
> >
> > Product details
> > ASIN : B0836F1YF6
> > Publication date : December 26, 2019
> > Language : English
> > File size : 741 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 175 pages
> > Lending : Enabled
> > Best Sellers Rank: #3,768,255 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #3,591 in Probability & Statistics (Kindle Store)
> > ◦ #19,091 in Probability & Statistics (Books)
> >
> >
> >
> > #5-7, 89th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 6 for age 21-22 Senior-year of College, math textbook series, book 7 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revision was 6Feb2021.
> > Preface: This is the last year of College for mathematics and we have to mostly summarize all of mathematics as best we can. And set a new pattern to prepare students going on to math graduate school. A new pattern of work habits, because graduate school is more of research and explore on your own. So in this final year, I am going to eliminate tests, and have it mostly done as homework assignments.
> >
> > Cover Picture: Again and again, many times in math, the mind is not good enough alone to think straight and clear, and you need tools to hands-on see how it works. Here is a collection of tools for this senior year college classes. There is a pencil, clipboard, graph paper, compass, divider, protractor, slide-ruler. And for this year we spend a lot of time on the parallelepiped, showing my wood model, and showing my erector set model held together by wire loops in the corners. The plastic square is there only to hold up the erector set model.
> >
> > Length: 110 pages
> >
> > Product details
> > ASIN : B084V11BGY
> > Publication date : February 15, 2020
> > Language : English
> > File size : 826 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Enabled
> > Print length : 110 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,965 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #345 in Mathematics (Kindle Store)
> > ◦ #373 in Physics (Kindle Store)
> > ◦ #2,256 in Physics (Books)
> >
> > #5-8, 90th published book
> >
> > TEACHING TRUE MATHEMATICS: Volume 7 for age 22-26 Graduate school, math textbook series, book 8 Kindle Edition
> > by Archimedes Plutonium 2020
> >
> > Last revised 1NOV2020. This was AP's 90th published book of science.
> >
> > Preface: This is College Graduate School mathematics. Congratulations, you made it this far. To me, graduate school is mostly research, research mathematics and that means also physics. So it is going to be difficult to do math without physics. Of course, we focus on the mathematics of these research projects.
> >
> > My textbook for Graduate school is just a template and the professors teaching the graduate students are free of course to follow their own projects, but in terms of being physics and math combined. What I list below is a template for possible projects.
> >
> > So, in the below projects, I list 36 possible research projects that a graduate student my like to undertake, or partake. I list those 36 projects with a set of parentheses like this (1), (2), (3), etc. Not to be confused with the chapters listing as 1), 2), 3), etc. I list 36 projects but the professor can offer his/her own list, and I expect students with their professor, to pick a project and to monitor the student as to his/her progresses through the research. I have listed each project then cited some of my own research into these projects, below each project is an entry. Those entries are just a help or helper in getting started or acquainted with the project. The entry has a date time group and a newsgroup that I posted to such as sci.math or plutonium-atom-universe Google newsgroups. Again the entry is just a help or helper in getting started.
> >
> > Now instead of picking one or two projects for your Graduate years of study, some may select all 36 projects where you write a short paper on each project. Some may be bored with just one or two projects and opt for all 36.
> >
> > Cover Picture: A photo by my iphone of a page on Permutations of the Jacobs book Mathematics: A Human Endeavor, 1970. One of the best textbooks ever written in Old Math, not for its contents because there are many errors, but for its teaching style. It is extremely rare to find a math textbook written for the student to learn. Probably because math professors rarely learned how to teach in the first place; only learned how to unintentionally obfuscate. The page I photographed is important because it is the interface between geometry's perimeter or surface area versus geometry's area or volume, respectively. Or, an interface of pure numbers with that of geometry. But I have more to say on this below.
> > Length: 296 pages
> >
> > Product details
> > ASIN : B085DF8R7V
> > Publication date : March 1, 2020
> > Language : English
> > File size : 828 KB
> > Text-to-Speech : Enabled
> > Screen Reader : Supported
> > Enhanced typesetting : Enabled
> > X-Ray : Not Enabled
> > Word Wise : Not Enabled
> > Print length : 296 pages
> > Lending : Enabled
> > Best Sellers Rank: #224,981 in Kindle Store (See Top 100 in Kindle Store)
> > ◦ #13 in General Geometry
> > ◦ #213 in Geometry & Topology (Books)
> >
> >
> >
> > #5-8, 160th published book
> >
> > MATHOPEDIA-- List of 80 fakes and mistakes of Old Math// Student teaches professor Kindle Edition
> > by Archimedes Plutonium (Author)
> >
> > Last revision was 28Apr2022. And this is AP's 160th book of Science.
> > Preface:
> > A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.
> > The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.
> > The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery. I know because I have been there.
> > Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.
> > I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).
> >
> > Product details
> > • ASIN : B09MZTLRL5
> > • Publication date : December 2, 2021
> > • Language : English
> > • File size : 1149 KB
> > • Text-to-Speech : Enabled
> > • Screen Reader : Supported
> > • Enhanced typesetting : Enabled
> > • X-Ray : Not Enabled
> > • Word Wise : Not Enabled
> > • Print length : 65 pages
> > • Lending : Enabled
Dan Christensen
Nov 24, 2022, 10:25:36 AM11/24/22
to
STUDENTS BEWARE: Don't be a victim of AP's fake math and science
On Thursday, November 24, 2022 at 2:20:47 AM UTC-5, Archimedes Plutonium wrote:
> >Dan Christensen...
[snip]
Time for another spanking, Archie Poo? When will you learn? Once again...
From his antics here at sci.math, it is obvious that AP has abandoned all hope of being recognized as a credible personality. He is a malicious internet troll who now wants only to mislead and confuse students. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives. Is it revenge for his endless string of personal failures in life? Who knows.
In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
“0/0 must be equal to 1.”
-- June 9, 2015
“0 is an infinite irrational number.”
--June 28, 2015
“No negative numbers exist.”
--December 22, 2018
“Rationals are not numbers.”
--May 18, 2019
According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019
Which could explain...
“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019
AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:
“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019
AP seeks aid of Russian agents to promote failure in schools:
"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--November 9, 2017
And if that wasn't weird enough...
“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994
“The Universe itself is one gigantic big atom.”
--November 14, 2019
AP's sinister Atom God Cult of Failure???
“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)
On Thursday, November 24, 2022 at 2:20:47 AM UTC-5, Archimedes Plutonium wrote:
> >Dan Christensen...
[snip]
Time for another spanking, Archie Poo? When will you learn? Once again...
From his antics here at sci.math, it is obvious that AP has abandoned all hope of being recognized as a credible personality. He is a malicious internet troll who now wants only to mislead and confuse students. He may not be all there, but his fake math and science can only be meant to promote failure in schools. One can only guess at his motives. Is it revenge for his endless string of personal failures in life? Who knows.
In AP's OWN WORDS here that, over the years, he has NEVER renounced or withdrawn:
“Primes do not exist, because the set they were borne from has no division.”
--June 29, 2020
“The last and largest finite number is 10^604.”
--June 3, 2015
“0 appears to be the last and largest finite number”
--June 9, 2015
“0/0 must be equal to 1.”
-- June 9, 2015
“0 is an infinite irrational number.”
--June 28, 2015
“No negative numbers exist.”
--December 22, 2018
“Rationals are not numbers.”
--May 18, 2019
According to AP's “chess board math,” an equilateral triangle is a right-triangle.
--December 11, 2019
Which could explain...
“The value of sin(45 degrees) = 1.” (Actually 0.707)
--May 31, 2019
AP deliberately and repeatedly presented the truth table for OR as the truth table for AND:
“New Logic
AND
T & T = T
T & F = T
F & T = T
F & F = F”
--November 9, 2019
AP seeks aid of Russian agents to promote failure in schools:
"Please--Asking for help from Russia-- russian robots-- to create a new, true mathematics [sic]. What I like for the robots to do, is list every day, about 4 Colleges ( of the West) math dept, and ask why that math department is teaching false and fake math, and if unable to change to the correct true math, well, simply fire that math department until they can find professors who recognize truth in math from fakery...."
--November 9, 2017
And if that wasn't weird enough...
“The totality, everything that there is [the universe], is only 1 atom of plutonium [Pu]. There is nothing outside or beyond this one atom of plutonium.”
--April 4, 1994
“The Universe itself is one gigantic big atom.”
--November 14, 2019
AP's sinister Atom God Cult of Failure???
“Since God-Pu is marching on.
Glory! Glory! Atom Plutonium!
Its truth is marching on.
It has sounded forth the trumpet that shall never call retreat;
It is sifting out the hearts of people before its judgment seat;
Oh, be swift, my soul, to answer it; be jubilant, my feet!
Our God-Pu is marching on.”
--December 15, 2018 (Note: Pu is the atomic symbol for plutonium)
Mostowski Collapse
Nov 24, 2022, 11:02:00 AM11/24/22
to
Ha Ha, if we were to ask Dan Christense to prove the
theorem "Every Planar Map is Four-Colorable", and if
we would give him that the colors are:
{red, green, blue, yellow}
He would possibly produce 4! = 24 proofs, depending
how the crayons are layed out on the table, for the
poor hypothetical guy who needs to color all the
infinitely many possible planar graph. LoL
theorem "Every Planar Map is Four-Colorable", and if
we would give him that the colors are:
{red, green, blue, yellow}
He would possibly produce 4! = 24 proofs, depending
how the crayons are layed out on the table, for the
poor hypothetical guy who needs to color all the
infinitely many possible planar graph. LoL
Dan Christensen
Nov 24, 2022, 11:18:43 AM11/24/22
to
On Thursday, November 24, 2022 at 11:02:00 AM UTC-5, Mostowski Collapse (Jan Burse) wrote:
> Ha Ha, if we were to ask Dan Christense to prove the
> theorem "Every Planar Map is Four-Colorable", and if
>
> we would give him that the colors are:
>
> {red, green, blue, yellow}
>
> He would possibly produce 4! = 24 proofs, depending
> how the crayons are layed out on the table, for the
>
> poor hypothetical guy who needs to color all the
> infinitely many possible planar graph.
Poor Jan Burse here claimed that there existed a formal, mathematical shortcut to a simple proof I had presented. (See original posting.) He failed and was unable to prove it. Now he can now only hope to muddy the waters by changing the subject. Really kind of pathetic.
> Ha Ha, if we were to ask Dan Christense to prove the
> theorem "Every Planar Map is Four-Colorable", and if
>
> we would give him that the colors are:
>
> {red, green, blue, yellow}
>
> He would possibly produce 4! = 24 proofs, depending
> how the crayons are layed out on the table, for the
>
> poor hypothetical guy who needs to color all the
> infinitely many possible planar graph.
Dan
Forest Vaccaro
Nov 24, 2022, 11:44:12 AM11/24/22
to
Mostowski Collapse wrote:
> Ha Ha, if we were to ask Dan Christense to prove the theorem "Every
> Planar Map is Four-Colorable", and if
> we would give him that the colors are:
> {red, green, blue, yellow}
don't talk with him. He's calling his wive *Michael* by "mistake".
> Ha Ha, if we were to ask Dan Christense to prove the theorem "Every
> Planar Map is Four-Colorable", and if
> we would give him that the colors are:
> {red, green, blue, yellow}
Mostowski Collapse
Nov 24, 2022, 11:46:39 AM11/24/22
to
Ok, we will help Wonky Man, to solve his homework.
Here are two lemmas, towards proving Crbxyz => Cbrxyz:
Lemma 1: Swap "either red or blue"
12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
Conclusion, 1
Lemma 2: Swap "two reds or two blues"
12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
& y=r]
Conclusion, 1
---------------------- begin proof -----------------------------------------
Lemma 1: Swap "either red or blue"
1 x=r | x=b
Premise
2 ~[x=b | x=r]
Premise
3 ~~[~x=b & ~x=r]
DeMorgan, 2
4 ~x=b & ~x=r
Rem DNeg, 3
5 ~x=b
Split, 4
6 ~x=r
Split, 4
7 ~x=r => x=b
Imply-Or, 1
8 x=b
Detach, 7, 6
9 ~x=b & x=b
Join, 5, 8
10 ~~[x=b | x=r]
Conclusion, 2
11 x=b | x=r
Rem DNeg, 10
12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
Conclusion, 1
Lemma 2: Swap "two reds or two blues"
1 x=r & y=r | x=b & y=b
Premise
2 ~[x=b & y=b | x=r & y=r]
Premise
3 ~~[~[x=b & y=b] & ~[x=r & y=r]]
DeMorgan, 2
4 ~[x=b & y=b] & ~[x=r & y=r]
Rem DNeg, 3
5 ~[x=b & y=b]
Split, 4
6 ~[x=r & y=r]
Split, 4
7 ~[x=r & y=r] => x=b & y=b
Imply-Or, 1
8 x=b & y=b
Detach, 7, 6
9 ~[x=b & y=b] & [x=b & y=b]
Join, 5, 8
10 ~~[x=b & y=b | x=r & y=r]
Conclusion, 2
11 x=b & y=b | x=r & y=r
Rem DNeg, 10
12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
& y=r]
Conclusion, 1
Dan Christensen schrieb:
Here are two lemmas, towards proving Crbxyz => Cbrxyz:
Lemma 1: Swap "either red or blue"
12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
Conclusion, 1
Lemma 2: Swap "two reds or two blues"
12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
& y=r]
Conclusion, 1
---------------------- begin proof -----------------------------------------
Lemma 1: Swap "either red or blue"
1 x=r | x=b
Premise
2 ~[x=b | x=r]
Premise
3 ~~[~x=b & ~x=r]
DeMorgan, 2
4 ~x=b & ~x=r
Rem DNeg, 3
5 ~x=b
Split, 4
6 ~x=r
Split, 4
7 ~x=r => x=b
Imply-Or, 1
8 x=b
Detach, 7, 6
9 ~x=b & x=b
Join, 5, 8
10 ~~[x=b | x=r]
Conclusion, 2
11 x=b | x=r
Rem DNeg, 10
12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
Conclusion, 1
Lemma 2: Swap "two reds or two blues"
1 x=r & y=r | x=b & y=b
Premise
2 ~[x=b & y=b | x=r & y=r]
Premise
3 ~~[~[x=b & y=b] & ~[x=r & y=r]]
DeMorgan, 2
4 ~[x=b & y=b] & ~[x=r & y=r]
Rem DNeg, 3
5 ~[x=b & y=b]
Split, 4
6 ~[x=r & y=r]
Split, 4
7 ~[x=r & y=r] => x=b & y=b
Imply-Or, 1
8 x=b & y=b
Detach, 7, 6
9 ~[x=b & y=b] & [x=b & y=b]
Join, 5, 8
10 ~~[x=b & y=b | x=r & y=r]
Conclusion, 2
11 x=b & y=b | x=r & y=r
Rem DNeg, 10
12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
& y=r]
Conclusion, 1
Dan Christensen schrieb:
Message has been deleted
Dan Christensen
Nov 24, 2022, 12:36:10 PM11/24/22
to
On Thursday, November 24, 2022 at 11:46:39 AM UTC-5, Mostowski Collapse wrote:
> Ok, we will help Wonky Man, to solve his homework.
> Here are two lemmas, towards proving Crbxyz => Cbrxyz:
>
> Lemma 1: Swap "either red or blue"
>
> 12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
> Conclusion, 1
>
> Lemma 2: Swap "two reds or two blues"
>
> 12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
> & y=r]
> Conclusion, 1
[snip]
> Ok, we will help Wonky Man, to solve his homework.
> Here are two lemmas, towards proving Crbxyz => Cbrxyz:
>
> Lemma 1: Swap "either red or blue"
>
> 12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
> Conclusion, 1
>
> Lemma 2: Swap "two reds or two blues"
>
> 12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
> & y=r]
> Conclusion, 1
How does this help establish of your supposed mathematical shortcut, Jan Burse? Recall that you will STILL need to establish, as on my line 96, that
color(x)=blue => EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
in significantly fewer than 31 lines to qualify as a "shortcut."
Mostowski Collapse
Nov 24, 2022, 12:46:17 PM11/24/22
to
See symmetry breaking theorem below. We can now make
some "without loss of generality" reasoning. Now you can prove:
/* Spezialize on red */
ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=r=> C(r,b,x,y,z))
This was already proved:
/* Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues" */
ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(C(r,b,x,y,z) => C(b,r,x,y,z))
Then you may automatically conclude:
/* Spezialize on blue */
ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=b=> C(r,b,x,y,z))
Yeah, its done! Even with clumsy tool like DC Poop.
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47 UTC+1:
> Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues"
> 29 ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r
> | [x=b & z=b | x=r & z=r]
> | [y=b & z=b | y=r & z=r]
> => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
> | [x=r & z=r | x=b & z=b]
> | [y=r & z=r | y=b & z=b]]]
> Conclusion, 3
> https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
some "without loss of generality" reasoning. Now you can prove:
/* Spezialize on red */
ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=r=> C(r,b,x,y,z))
This was already proved:
/* Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues" */
ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(C(r,b,x,y,z) => C(b,r,x,y,z))
Then you may automatically conclude:
/* Spezialize on blue */
ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=b=> C(r,b,x,y,z))
Yeah, its done! Even with clumsy tool like DC Poop.
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47 UTC+1:
> Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues"
> 29 ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r
> | [x=b & z=b | x=r & z=r]
> | [y=b & z=b | y=r & z=r]
> => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
> | [x=r & z=r | x=b & z=b]
> | [y=r & z=r | y=b & z=b]]]
> Conclusion, 3
> https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
Dan Christensen
Nov 24, 2022, 12:58:51 PM11/24/22
to
On Thursday, November 24, 2022 at 12:46:17 PM UTC-5, Mostowski Collapse wrote:
> Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47 UTC+1:
> > Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues"
> > 29 ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r
> > | [x=b & z=b | x=r & z=r]
> > | [y=b & z=b | y=r & z=r]
> > => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
> > | [x=r & z=r | x=b & z=b]
> > | [y=r & z=r | y=b & z=b]]]
> > Conclusion, 3
> > https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
> On Thursday, November 24, 2022 at 11:46:39 AM UTC-5, Mostowski Collapse wrote:
> > Ok, we will help Wonky Man, to solve his homework.
> > Here are two lemmas, towards proving Crbxyz => Cbrxyz:
> >
> > Lemma 1: Swap "either red or blue"
> >
> > 12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
> > Conclusion, 1
> >
> > Lemma 2: Swap "two reds or two blues"
> >
> > 12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
> > & y=r]
> > Conclusion, 1
> Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47 UTC+1:
> > Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues"
> > 29 ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r
> > | [x=b & z=b | x=r & z=r]
> > | [y=b & z=b | y=r & z=r]
> > => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
> > | [x=r & z=r | x=b & z=b]
> > | [y=r & z=r | y=b & z=b]]]
> > Conclusion, 3
> > https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
> On Thursday, November 24, 2022 at 11:46:39 AM UTC-5, Mostowski Collapse wrote:
> > Ok, we will help Wonky Man, to solve his homework.
> > Here are two lemmas, towards proving Crbxyz => Cbrxyz:
> >
> > Lemma 1: Swap "either red or blue"
> >
> > 12 ALL(x):ALL(r):ALL(b):[x=r | x=b => x=b | x=r]
> > Conclusion, 1
> >
> > Lemma 2: Swap "two reds or two blues"
> >
> > 12 ALL(x):ALL(r):ALL(y):ALL(b):[x=r & y=r | x=b & y=b => x=b & y=b | x=r
> > & y=r]
> > Conclusion, 1
> See symmetry breaking theorem below. We can now make
> some "without loss of generality" reasoning. Now you can prove:
>
> /* Spezialize on red */
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=r=> C(r,b,x,y,z))
>
> This was already proved:
>
> /* Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues" */
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(C(r,b,x,y,z) => C(b,r,x,y,z))
>
> Then you may automatically conclude:
>
> /* Spezialize on blue */
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=b=> C(r,b,x,y,z))
>
> Yeah, its done! [snip childish abuse]
> some "without loss of generality" reasoning. Now you can prove:
>
> /* Spezialize on red */
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=r=> C(r,b,x,y,z))
>
> This was already proved:
>
> /* Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues" */
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(C(r,b,x,y,z) => C(b,r,x,y,z))
>
> Then you may automatically conclude:
>
> /* Spezialize on blue */
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):(x=b=> C(r,b,x,y,z))
>
Not even started, Jan Burse. Again, you need to establish that:
color(x)=blue => EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
Mostowski Collapse
Nov 24, 2022, 3:33:35 PM11/24/22
to
No I don't need. Wikipedia says nowhere that there is
a function color. When you have 3 objects, you can
use variables x,y,z for their colors. Just read Wikipedia:
"If three objects are each painted either red or blue, then
there must be at least two objects of the same color."
https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
Whats wrong with you Wonky Man? Did your brain get evacuated?
a function color. When you have 3 objects, you can
use variables x,y,z for their colors. Just read Wikipedia:
"If three objects are each painted either red or blue, then
there must be at least two objects of the same color."
Whats wrong with you Wonky Man? Did your brain get evacuated?
Dan Christensen
Nov 24, 2022, 4:39:03 PM11/24/22
to
> No I don't need. Wikipedia says nowhere that there is
> a function color.
HA, HA! Grasping at straws, Jan Burse???
> a function color.
> When you have 3 objects, you can
> use variables x,y,z for their colors. Just read Wikipedia:
> "If three objects are each painted either red or blue, then
> there must be at least two objects of the same color."
> https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
>
It seems you have failed again, Jan Burse. Oh, well...
Don't feel bad. A good 1% of your postings here are really worthwhile. More than most.
Mostowski Collapse
Nov 24, 2022, 5:01:00 PM11/24/22
to
Hey Wonky Man is your DC Proof tool made of chinesium?
It seems to be extremly fragile, can even not prove the simplest
things. And how do you think the Pigeonhole principle is formulate
in a SAT Solver?
Ask pehou...@gmail.com he will tell you. If you have two boxes
red and blue, and 3 pingeons. So its a Pingeon(2,3) problem,
how will it be formulate? With a function color?
LMAO!
It seems to be extremly fragile, can even not prove the simplest
things. And how do you think the Pigeonhole principle is formulate
in a SAT Solver?
Ask pehou...@gmail.com he will tell you. If you have two boxes
red and blue, and 3 pingeons. So its a Pingeon(2,3) problem,
how will it be formulate? With a function color?
LMAO!
Mostowski Collapse
Nov 24, 2022, 5:12:22 PM11/24/22
to
You will even have more variables if we would do the Pigeonhole principle:
> State of affair is represented as:
> Xij <=> pigeon i is placed in hole j i in 0..n-1, j in 0..m-1
> Clause for each pigeon that it is placed in at least one hole:
> Xi0 v .. v Xim-1 i in 0..n-1
> Clauses for each hole that it carries maximally one pigeon:
> ~Xij v ~Xkj i in 0..n-1, k in i+1..n-1, j in 0..m-1.
> Should work correctly for n>=m.
The outcome for two boxes red and blue, will be basically
that you cannot place 3 pigeons each in its own box.
So we have n=3, m=2. This gives a matrice of 3x2 variables:
X11 X12
X21 X22
X31 X32
And the boolean conditions are:
X11 v X12
X21 v X22
X31 v X32
~X11 v ~X21
~X11 v ~X31
~X21 v ~X31
~X12 v ~X22
~X12 v ~X32
~X22 v ~X32
So using a SAT solvere for example from SWI-Prolog we get:
?- use_module(library(clpb)).
true.
?- sat((X11+X12)*
(X21+X22)*
(X31+X32)*
(~X11+ ~X21)*
(~X11+ ~X31)*
(~X21+ ~X31)*
(~X12+ ~X22)*
(~X12+ ~X32)*
(~X22+ ~X32)).
false.
> State of affair is represented as:
> Xij <=> pigeon i is placed in hole j i in 0..n-1, j in 0..m-1
> Clause for each pigeon that it is placed in at least one hole:
> Xi0 v .. v Xim-1 i in 0..n-1
> Clauses for each hole that it carries maximally one pigeon:
> ~Xij v ~Xkj i in 0..n-1, k in i+1..n-1, j in 0..m-1.
> Should work correctly for n>=m.
The outcome for two boxes red and blue, will be basically
that you cannot place 3 pigeons each in its own box.
So we have n=3, m=2. This gives a matrice of 3x2 variables:
X11 X12
X21 X22
X31 X32
And the boolean conditions are:
X11 v X12
X21 v X22
X31 v X32
~X11 v ~X21
~X11 v ~X31
~X21 v ~X31
~X12 v ~X22
~X12 v ~X32
~X22 v ~X32
So using a SAT solvere for example from SWI-Prolog we get:
?- use_module(library(clpb)).
true.
?- sat((X11+X12)*
(X21+X22)*
(X31+X32)*
(~X11+ ~X21)*
(~X11+ ~X31)*
(~X21+ ~X31)*
(~X12+ ~X22)*
(~X12+ ~X32)*
(~X22+ ~X32)).
false.
Mostowski Collapse
Nov 24, 2022, 5:16:20 PM11/24/22
to
So lets sum up why DC Proof is made of chinesium:
- Failure 1: Wonky Man cannot use his own take
with a color function, to show a WLOG inference.
- Failure 2: Wonky Man is not able to understand
the 3 variables x,y,z solution that shows a WLOG inference.
- Failure 3: Given Failure 1 and Failure 2, I guess
a SAT solver Pigeon principle is also out of reach for Wonky Man.
- Failure 1: Wonky Man cannot use his own take
with a color function, to show a WLOG inference.
- Failure 2: Wonky Man is not able to understand
the 3 variables x,y,z solution that shows a WLOG inference.
- Failure 3: Given Failure 1 and Failure 2, I guess
a SAT solver Pigeon principle is also out of reach for Wonky Man.
Dan Christensen
Nov 24, 2022, 5:52:49 PM11/24/22
to
On Thursday, November 24, 2022 at 5:16:20 PM UTC-5, Mostowski Collapse wrote:
> So lets sum up why DC Proof is made of chinesium:
>
> - Failure 1: [snip childish abuse] cannot use his own take
> So lets sum up why DC Proof is made of chinesium:
>
> with a color function, to show a WLOG inference.
>
See the subject line here, Jan Burse. I make no claim of any kind formal shortcut based WLOG. Quite the contrary. You, on the other claimed you had found such a shortcut. Alas, it didn't pan out. You had failed once again.
>
> - Failure 2: [snip childish abuse] is not able to understand
> the 3 variables x,y,z solution that shows a WLOG inference.
>
Poor Jan Burse could not prove the case of the first object being blue using his supposed shortcut. He thinks he doesn't have to. Really kind of pathetic. Yet another failure.
>
> - Failure 3: Given Failure 1 and Failure 2, I guess
See https://dcproof.wordpress.com/2013/05/04/dedekinds-pigeons/
Fritz Feldhase
Nov 24, 2022, 7:00:39 PM11/24/22
to
On Thursday, November 24, 2022 at 8:16:47 AM UTC+1, Fritz Feldhase wrote:
> On Thursday, November 24, 2022 at 8:07:06 AM UTC+1, Fritz Feldhase wrote:
> > On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> > >
> > > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
> AM(card(M) = 3 & Am(m e M -> red(m) | blue(m)) -> card({m e M : red(m)} >= 2 v card({m e M : blue(m)} >= 2).
Even better:
> On Thursday, November 24, 2022 at 8:07:06 AM UTC+1, Fritz Feldhase wrote:
> > On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> > >
> > > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
> AM(card(M) = 3 & Am(m e M -> red(m) | blue(m)) -> card({m e M : red(m)} >= 2 v card({m e M : blue(m)} >= 2).
AM(|M| = 3 & Am(m e M -> m e Red | m e Blue) -> |M n Red| >= 2 v |M n Blue| >= 2
with: P | Q =def (P v Q) & ~(P & Q).
Fritz Feldhase
Nov 25, 2022, 12:15:44 AM11/25/22
to
On Friday, November 25, 2022 at 1:00:39 AM UTC+1, Fritz Feldhase wrote:
> > > On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> > > >
> > > > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
How about:
> > > On Monday, November 21, 2022 at 9:12:04 PM UTC+1, Dan Christensen wrote:
> > > >
> > > > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
AM: |M| = 3 & Am(m e M -> color(m) e {red, blue}) -> EmEn(m e M & n e M & m =/= n & color(m) = color(n)).
Fritz Feldhase
Nov 25, 2022, 12:34:57 AM11/25/22
to
On Thursday, November 24, 2022 at 9:33:35 PM UTC+1, Mostowski Collapse wrote:
> Wikipedia says nowhere that there is a function color.
So what? We may consider the /color/ of an object an intrinsic property of it. Remember functions and, say, their domain? (There we might refer to the domain of a function f with dom(f). In the same way we may refer to the color of an object o with color(o).)
> Wikipedia says nowhere that there is a function color.
AM: |M| = 3 & Am(m e M -> color(m) e {red, blue}) -> EmEn(m e M & n e M & m =/= n & color(m) = color(n)).
"If three objects are each painted either red or blue, then there must be at least two objects of the same color."
Of course we may work with sets of objects of a certain color as well, in this case we would have, say,
x e Red <-> color(x) = red and x e Blue <-> color(x) = blue .
"x is (a) red (object) iff its color is red" and "x is (a) blue (object) iff its color is blue".
No?
Dan Christensen
Nov 25, 2022, 1:24:06 AM11/25/22
to
In lines 1-13, I effectively define:
s = {x, y, z}
colors = {red, blue}
color: s --> colors
But this isn't the issue here. I proved the required result by considering two cases: (1) color(x)=red, and (2) color(x)=blue. I proved both by a similar "brute force" method looking at all possible colorings. Jan Burse claims, but cannot formally prove, that proof of the 2nd case can be skipped by using a "shortcut" based on a proof "without loss of generality." I don't think he quite understands what that means. I think it isn't something that can be generally formalized. It is an INFORMAL shortcut that relies on the experience of the reader to recognize the intuitive symmetry of the situation. In this case, it is "intuitively obvious" that it shouldn't matter which color you choose to consider first. But how to formalize that notion in simple, efficient way? There's the rub!
Mostowski Collapse
Nov 25, 2022, 2:36:12 AM11/25/22
to
You are a liar, again and again. Of couse we can prove
your result, you asshole, your are only too stupid.
Its very easy, if you have 3 objects u,v,w,
and their colors color(u)=x, color(v)=y, color(w)=z.
Then if you prove a theorem P(x,y,z) about these
colors, then its also a theorem P(color(u),color(v),color(w)).
Whats wrong with you? See here:
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 21:59:06 UTC+1:
> The theorem works also in Wolfgang Schwartz tree tool:
> ∀x∀y∀zPxyz → ∀u∀v∀wPc(u)c(v)c(w) is valid.
> https://www.umsu.de/trees/#~6x~6y~6zP%28x,y,z%29~5~6u~6v~6wP%28c%28u%29,c%28v%29,c%28w%29%29
> With the advantage that the ALL(x):color(x) ε c isn't needed.
> https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/IOpQr52aBgAJ
your result, you asshole, your are only too stupid.
Its very easy, if you have 3 objects u,v,w,
and their colors color(u)=x, color(v)=y, color(w)=z.
Then if you prove a theorem P(x,y,z) about these
colors, then its also a theorem P(color(u),color(v),color(w)).
Whats wrong with you? See here:
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 21:59:06 UTC+1:
> The theorem works also in Wolfgang Schwartz tree tool:
> ∀x∀y∀zPxyz → ∀u∀v∀wPc(u)c(v)c(w) is valid.
> https://www.umsu.de/trees/#~6x~6y~6zP%28x,y,z%29~5~6u~6v~6wP%28c%28u%29,c%28v%29,c%28w%29%29
> With the advantage that the ALL(x):color(x) ε c isn't needed.
> https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/IOpQr52aBgAJ
Dan Christensen
Nov 25, 2022, 3:20:59 PM11/25/22
to
On Friday, November 25, 2022 at 2:36:12 AM UTC-5, Mostowski Collapse wrote:
> You are a liar, again and again. Of couse we can prove
> your result
Here's your assignment, Jan Burse:
> You are a liar, again and again. Of couse we can prove
> your result
Using DC Proof or the system of natural deduction of your choice, and your WLOG shortcut, formally prove:
EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
Define: s = {x, y, z}
1 Set(s)
Axiom
2 x in s
Axiom
3 y in s
Axiom
4 z in s
Axiom
5 ~x=y
Axiom
6 ~x=z
Axiom
7 ~y=z
Axiom
8 ALL(a):[a in s <=> a=x | a=y | a=z]
Axiom
Define: colors = {red, blue}
9 Set(colors)
Axiom
10 red in colors
Axiom
11 blue in colors
Axiom
12 ~red=blue
Axiom
13 ALL(a):[a in colors <=> a=red | a=blue]
Axiom
Define: The color function, color: s --> colors
14 ALL(a):[a in s => color(a) in colors]
Axiom
Previous results (optional)
15 color(x)=red | color(x)=blue
Axiom
16 color(x)=red
=> EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
Axiom
Good luck.
Micheal Agnelli
Nov 25, 2022, 3:47:40 PM11/25/22
to
Dan Christensen wrote:
> On Friday, November 25, 2022 at 2:36:12 AM UTC-5, Mostowski Collapse
> wrote:
>> You are a liar, again and again. Of couse we can prove your result
>
> Here's your assignment, Jan Burse:
> Using DC Proof or the system of natural deduction of your choice, and
> your WLOG shortcut, formally prove:
> EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
watch this penguin here, he is a repugnant repulsive subhuman
> On Friday, November 25, 2022 at 2:36:12 AM UTC-5, Mostowski Collapse
> wrote:
>> You are a liar, again and again. Of couse we can prove your result
>
> Here's your assignment, Jan Burse:
> Using DC Proof or the system of natural deduction of your choice, and
> your WLOG shortcut, formally prove:
> EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
*_terrorist_*. Go tell them, I sent you to say that. These nazi mazafakars
*_state_driven_terrorists_* war_criminals, most likely be erased from the
face of the earth. They don't even know yet what they are dealing with.
They think it's Iraq, Afghanistan or Libya.
UK urges Ukraine to ‘maintain momentum’ through winter
https://%72%74.com/news/567177-wallace-offensive-ukraine-winter/
According to the British defense secretary, Kiev has received “300,000
pieces of arctic warfare kit” from its backers
Mostowski Collapse
Nov 26, 2022, 8:28:04 AM11/26/22
to
Whats your prolololoblem Wonky Man? Still level 1000 stupid?
Thats your assignment. Moron. Its relatively trivial with x,y,z colors.
so we prove towards ultimately proving: First recall what is
our goal, what we want to prove, call the logical matrice of it by the
name C(r,b,x,y,z), the logical matrice is what is inside the quantifier block:
Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
ALL(x):ALL(y):ALL(z):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
different logical matrice, namely x=r => C(r,b,x,y,z). Quite trivial:
53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r =>
------------------------------- begin proof -----------------------------
1 ~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Premise
2 ~~[x=r & ~[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Imply-And, 1
3 x=r & ~[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]
Rem DNeg, 2
4 x=r
Split, 3
5 ~[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]
Split, 3
6 ~[[r=r | r=b] & [y=r | y=b] & [z=r | z=b] => r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]
Substitute, 4, 5
7 ~~[[r=r | r=b] & [y=r | y=b] & [z=r | z=b] & ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]]
Imply-And, 6
8 [r=r | r=b] & [y=r | y=b] & [z=r | z=b] & ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]
Rem DNeg, 7
9 r=r | r=b
Split, 8
10 y=r | y=b
Split, 8
11 z=r | z=b
Split, 8
12 ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]
Split, 8
13 ~~[~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b]] & ~[y=r & z=r | y=b & z=b]]
DeMorgan, 12
14 ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b]] & ~[y=r & z=r | y=b & z=b]
Rem DNeg, 13
15 ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b]]
Split, 14
16 ~[y=r & z=r | y=b & z=b]
Split, 14
17 ~~[~[r=r & y=r | r=b & y=b] & ~[r=r & z=r | r=b & z=b]]
DeMorgan, 15
18 ~[r=r & y=r | r=b & y=b] & ~[r=r & z=r | r=b & z=b]
Rem DNeg, 17
19 ~[r=r & y=r | r=b & y=b]
Split, 18
20 ~[r=r & z=r | r=b & z=b]
Split, 18
21 y=r
Premise
22 ~[r=r & r=r | r=b & r=b]
Substitute, 21, 19
23 r=r
Reflex
24 r=r & r=r
Join, 23, 23
25 r=r & r=r | r=b & r=b
Arb Or, 24
26 ~[r=r & r=r | r=b & r=b] & [r=r & r=r | r=b & r=b]
Join, 22, 25
27 ~y=r
Conclusion, 21
28 ~y=r => y=b
Imply-Or, 10
29 y=b
Detach, 28, 27
30 z=r
Premise
31 ~[r=r & r=r | r=b & r=b]
Substitute, 30, 20
32 r=r
Reflex
33 r=r & r=r
Join, 32, 32
34 r=r & r=r | r=b & r=b
Arb Or, 33
35 ~[r=r & r=r | r=b & r=b] & [r=r & r=r | r=b & r=b]
Join, 31, 34
36 ~z=r
Conclusion, 30
37 ~z=r => z=b
Imply-Or, 11
38 z=b
Detach, 37, 36
39 y=b & z=b
Join, 29, 38
40 y=r & z=r | y=b & z=b
Arb Or, 39
41 ~[y=r & z=r | y=b & z=b] & [y=r & z=r | y=b & z=b]
Join, 16, 40
42 ~EXIST(x):EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Conclusion, 1
43 ~~ALL(x):~EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 42
44 ALL(x):~EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 43
45 ALL(x):~~ALL(r):~EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 44
46 ALL(x):ALL(r):~EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 45
47 ALL(x):ALL(r):~~ALL(b):~EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 46
48 ALL(x):ALL(r):ALL(b):~EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 47
49 ALL(x):ALL(r):ALL(b):~~ALL(y):~EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 48
50 ALL(x):ALL(r):ALL(b):ALL(y):~EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 49
51 ALL(x):ALL(r):ALL(b):ALL(y):~~ALL(z):~~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 50
52 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):~~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 51
53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 52
------------------------------- end proof ---------------------------------------
Thats your assignment. Moron. Its relatively trivial with x,y,z colors.
so we prove towards ultimately proving: First recall what is
our goal, what we want to prove, call the logical matrice of it by the
name C(r,b,x,y,z), the logical matrice is what is inside the quantifier block:
Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
ALL(x):ALL(y):ALL(z):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
And intermediate step, that you seem to have requested, is to prove a
different logical matrice, namely x=r => C(r,b,x,y,z). Quite trivial:
53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r =>
[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 52
x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
------------------------------- begin proof -----------------------------
1 ~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Premise
2 ~~[x=r & ~[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Imply-And, 1
3 x=r & ~[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]
Rem DNeg, 2
4 x=r
Split, 3
5 ~[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]
Split, 3
6 ~[[r=r | r=b] & [y=r | y=b] & [z=r | z=b] => r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]
Substitute, 4, 5
7 ~~[[r=r | r=b] & [y=r | y=b] & [z=r | z=b] & ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]]
Imply-And, 6
8 [r=r | r=b] & [y=r | y=b] & [z=r | z=b] & ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]
Rem DNeg, 7
9 r=r | r=b
Split, 8
10 y=r | y=b
Split, 8
11 z=r | z=b
Split, 8
12 ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b] | [y=r & z=r | y=b & z=b]]
Split, 8
13 ~~[~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b]] & ~[y=r & z=r | y=b & z=b]]
DeMorgan, 12
14 ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b]] & ~[y=r & z=r | y=b & z=b]
Rem DNeg, 13
15 ~[r=r & y=r | r=b & y=b | [r=r & z=r | r=b & z=b]]
Split, 14
16 ~[y=r & z=r | y=b & z=b]
Split, 14
17 ~~[~[r=r & y=r | r=b & y=b] & ~[r=r & z=r | r=b & z=b]]
DeMorgan, 15
18 ~[r=r & y=r | r=b & y=b] & ~[r=r & z=r | r=b & z=b]
Rem DNeg, 17
19 ~[r=r & y=r | r=b & y=b]
Split, 18
20 ~[r=r & z=r | r=b & z=b]
Split, 18
21 y=r
Premise
22 ~[r=r & r=r | r=b & r=b]
Substitute, 21, 19
23 r=r
Reflex
24 r=r & r=r
Join, 23, 23
25 r=r & r=r | r=b & r=b
Arb Or, 24
26 ~[r=r & r=r | r=b & r=b] & [r=r & r=r | r=b & r=b]
Join, 22, 25
27 ~y=r
Conclusion, 21
28 ~y=r => y=b
Imply-Or, 10
29 y=b
Detach, 28, 27
30 z=r
Premise
31 ~[r=r & r=r | r=b & r=b]
Substitute, 30, 20
32 r=r
Reflex
33 r=r & r=r
Join, 32, 32
34 r=r & r=r | r=b & r=b
Arb Or, 33
35 ~[r=r & r=r | r=b & r=b] & [r=r & r=r | r=b & r=b]
Join, 31, 34
36 ~z=r
Conclusion, 30
37 ~z=r => z=b
Imply-Or, 11
38 z=b
Detach, 37, 36
39 y=b & z=b
Join, 29, 38
40 y=r & z=r | y=b & z=b
Arb Or, 39
41 ~[y=r & z=r | y=b & z=b] & [y=r & z=r | y=b & z=b]
Join, 16, 40
42 ~EXIST(x):EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Conclusion, 1
43 ~~ALL(x):~EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 42
44 ALL(x):~EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 43
45 ALL(x):~~ALL(r):~EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 44
46 ALL(x):ALL(r):~EXIST(b):EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 45
47 ALL(x):ALL(r):~~ALL(b):~EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 46
48 ALL(x):ALL(r):ALL(b):~EXIST(y):EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 47
49 ALL(x):ALL(r):ALL(b):~~ALL(y):~EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 48
50 ALL(x):ALL(r):ALL(b):ALL(y):~EXIST(z):~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 49
51 ALL(x):ALL(r):ALL(b):ALL(y):~~ALL(z):~~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Quant, 50
52 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):~~[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 51
53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
Rem DNeg, 52
------------------------------- end proof ---------------------------------------
Dan Christensen
Nov 26, 2022, 9:30:33 AM11/26/22
to
On Saturday, November 26, 2022 at 8:28:04 AM UTC-5, Mostowski Collapse wrote:
[snip childish abuse]
Its relatively trivial with x,y,z colors.
> so we prove towards ultimately proving: First recall what is
>
> our goal, what we want to prove, call the logical matrice of it by the
> name C(r,b,x,y,z), the logical matrice is what is inside the quantifier block:
>
> Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> ALL(x):ALL(y):ALL(z):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
> And intermediate step, that you seem to have requested, is to prove a
> different logical matrice, namely x=r => C(r,b,x,y,z). Quite trivial:
>
[snip]
I'm sure there are several ways to obtain the required result, but you were supposed to use your WLOG shortcut to obtain from the above axioms that:
EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
How about it, Jan Burse? If that is not possible, or too difficult, just say so.
It your "shortcut" is more than 31 lines, it really isn't much of a shortcut.
[snip childish abuse]
Its relatively trivial with x,y,z colors.
> so we prove towards ultimately proving: First recall what is
>
> our goal, what we want to prove, call the logical matrice of it by the
> name C(r,b,x,y,z), the logical matrice is what is inside the quantifier block:
>
> Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> ALL(x):ALL(y):ALL(z):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
> And intermediate step, that you seem to have requested, is to prove a
> different logical matrice, namely x=r => C(r,b,x,y,z). Quite trivial:
>
I'm sure there are several ways to obtain the required result, but you were supposed to use your WLOG shortcut to obtain from the above axioms that:
EXIST(a):EXIST(b):[a in s & b in s & [~a=b & color(a)=color(b)]]
It your "shortcut" is more than 31 lines, it really isn't much of a shortcut.
Mostowski Collapse
Nov 26, 2022, 10:17:08 AM11/26/22
to
Its shown here in this thread how its done:
> Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
>
> ALL(x):[x in c <=> x=r v x=b]
> color(u) in c & color(v) in c & color(w) in c
> ~u=v & ~u=w & ~v=w
>
> To arrive at:
>
> EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/gWDsq2DABgAJ
Now if you can prove the theorem without using x=red and x=blue
essentially same proof twice, then you can also prove
EXIST(p):EXIST(q):[~p=q => color(p)=color(q)] without using
essentially same proof twice.
Or do you disagree on this observation?
> Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
>
> Its then an easy corollary, from the additional assumptions:
>
>
> ALL(x):[x in c <=> x=r v x=b]
> color(u) in c & color(v) in c & color(w) in c
> ~u=v & ~u=w & ~v=w
>
> To arrive at:
>
> EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/gWDsq2DABgAJ
Now if you can prove the theorem without using x=red and x=blue
essentially same proof twice, then you can also prove
EXIST(p):EXIST(q):[~p=q => color(p)=color(q)] without using
essentially same proof twice.
Or do you disagree on this observation?
Dan Christensen
Nov 26, 2022, 1:29:00 PM11/26/22
to
On Saturday, November 26, 2022 at 10:17:08 AM UTC-5, Mostowski Collapse wrote:
> Its shown here in this thread how its done:
> > Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> > ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> > x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
> >
> > Its then an easy corollary, from the additional assumptions:
> >
> > ALL(x):[x in c <=> x=r v x=b]
> > color(u) in c & color(v) in c & color(w) in c
> > ~u=v & ~u=w & ~v=w
> >
> > To arrive at:
> >
> > EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
> https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/gWDsq2DABgAJ
>
> Now if you can prove the theorem without using x=red and x=blue
> essentially same proof twice, then you can also prove
> EXIST(p):EXIST(q):[~p=q => color(p)=color(q)] without using
> essentially same proof twice.
>
[snip]
> Its shown here in this thread how its done:
> > Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> > ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> > x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
> >
> > Its then an easy corollary, from the additional assumptions:
> >
> > ALL(x):[x in c <=> x=r v x=b]
> > color(u) in c & color(v) in c & color(w) in c
> > ~u=v & ~u=w & ~v=w
> >
> > To arrive at:
> >
> > EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
> https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/gWDsq2DABgAJ
>
> Now if you can prove the theorem without using x=red and x=blue
> essentially same proof twice, then you can also prove
> EXIST(p):EXIST(q):[~p=q => color(p)=color(q)] without using
> essentially same proof twice.
>
Unless I have missed something, it seems you have given up on your WLOG proof, Jan Burse. When it comes to formal WLOG proofs, it seems you will need some kind axiom schema(s) for various types of proofs that exploit some kind of symmetry. I see nothing like that in your proofs here.
Dan Christensen
Nov 26, 2022, 4:01:41 PM11/26/22
to
Ross A. Finlayson
Nov 26, 2022, 8:17:19 PM11/26/22
to
On Monday, November 21, 2022 at 2:22:23 PM UTC-8, Ross A. Finlayson wrote:
> On Monday, November 21, 2022 at 1:23:29 PM UTC-8, Mike Terry wrote:
> > On 21/11/2022 20:11, Dan Christensen wrote:
> > > What is meant by "without loss of generality" in a mathematical proof?
> > >
> > > "In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
> > >
> > > "Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
> > > --George Bergman
> > > https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
> > >
> > > Here I formally prove the following theorem from Wikipedia:
> > >
> > > "A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
> > >
> > > https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
> > >
> > > Formally, I prove (link below):
> > >
> > > EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
> > >
> > > Where
> > >
> > > s = a set of 3 distinct elements: {x, y, z}
> > >
> > > colors = a set of 2 distinct elements: {red, blue}
> > >
> > > color(n) = the color of object n
> > >
> > > I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
> > I would have thought the two sub-proofs should be /obviously/ alike - there's a symmetry in the
> > problem between red <--> blue.
> >
> > >
> > > It seems unlikely that the without-loss-of-generality claim can be justified using the ordinary rules of logic [...]
> >
> > WLOG is a kind of meta-proving strategy that cuts down the size of a proof so that it is clearer, or
> > more easily followed by the reader. E.g. it might exploit some symmetry in the problem to save the
> > reader from ploughing through many scenarios with essentially similar logic. Or it might identify a
> > superficially simpler scenario to deal with, with it being clear to the reader that proof of the
> > simpler scenario would readily enable proof of the full claim of the theorem.
> >
> > It's expected that the reader will understand how the shortened proof would be expanded to a full
> > (more formal) proof, so the WLOG usage /could/ be completely avoided if required. That's why I
> > described it as a "meta-proving" strategy.
> >
> > The logical justification behind the usage is that it is indeed seen by the reader that the longer
> > proof (without using WLOG) works. However, encapsulating precisely /why/ it works in one single
> > justification seems implausible. Within a formal proof system, the proof could just follow the
> > expanded proof without mentioning WLOG. (Hopefully you weren't suggesting there was anything
> > "fishy" about proofs phrased using WLOG.)
> >
> > Regards,
> > Mike.
> What you're talking about there is "strongly defined types".
>
> And loosely defined, ....
>
> Naifs.
"Without loss of generality" is easily defineable,
it's called type theory and extensionality.
> On Monday, November 21, 2022 at 1:23:29 PM UTC-8, Mike Terry wrote:
> > On 21/11/2022 20:11, Dan Christensen wrote:
> > > What is meant by "without loss of generality" in a mathematical proof?
> > >
> > > "In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
> > >
> > > "Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
> > > --George Bergman
> > > https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
> > >
> > > Here I formally prove the following theorem from Wikipedia:
> > >
> > > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
> > >
> > > Wikipeda provides the following INFORMAL proof:
> > > "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
> > >
> > >
> > > "A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
> > >
> > > https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
> > >
> > > Formally, I prove (link below):
> > >
> > > EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
> > >
> > > Where
> > >
> > > s = a set of 3 distinct elements: {x, y, z}
> > >
> > > colors = a set of 2 distinct elements: {red, blue}
> > >
> > > color(n) = the color of object n
> > >
> > > I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
> > I would have thought the two sub-proofs should be /obviously/ alike - there's a symmetry in the
> > problem between red <--> blue.
> >
> > >
> > > It seems unlikely that the without-loss-of-generality claim can be justified using the ordinary rules of logic [...]
> >
> > WLOG is a kind of meta-proving strategy that cuts down the size of a proof so that it is clearer, or
> > more easily followed by the reader. E.g. it might exploit some symmetry in the problem to save the
> > reader from ploughing through many scenarios with essentially similar logic. Or it might identify a
> > superficially simpler scenario to deal with, with it being clear to the reader that proof of the
> > simpler scenario would readily enable proof of the full claim of the theorem.
> >
> > It's expected that the reader will understand how the shortened proof would be expanded to a full
> > (more formal) proof, so the WLOG usage /could/ be completely avoided if required. That's why I
> > described it as a "meta-proving" strategy.
> >
> > The logical justification behind the usage is that it is indeed seen by the reader that the longer
> > proof (without using WLOG) works. However, encapsulating precisely /why/ it works in one single
> > justification seems implausible. Within a formal proof system, the proof could just follow the
> > expanded proof without mentioning WLOG. (Hopefully you weren't suggesting there was anything
> > "fishy" about proofs phrased using WLOG.)
> >
> > Regards,
> > Mike.
> What you're talking about there is "strongly defined types".
>
> And loosely defined, ....
>
> Naifs.
"Without loss of generality" is easily defineable,
it's called type theory and extensionality.
Dan Christensen
Nov 26, 2022, 9:14:16 PM11/26/22
to
Mostowski Collapse
Nov 27, 2022, 5:26:26 AM11/27/22
to
Yeah, you missed it. I have completed the proof. See here:
Mostowski Collapse schrieb am Samstag, 26. November 2022 um 16:50:16 UTC+1:
> 117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
> Rem DNeg, 116
https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/skDAmuwmBwAJ
The last step is to show that, from these already proved two theorems:
> Theorem "Specialization to r"
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/w-98GSofBwAJ
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47 UTC+1:
> Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues"
> 29 ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r
> | [x=b & z=b | x=r & z=r]
> | [y=b & z=b | y=r & z=r]
> => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
We can deduce:
Theorem "Specialization to b"
ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b =>
is used in the first proof.
Easy, isn't it?
Mostowski Collapse schrieb am Samstag, 26. November 2022 um 16:50:16 UTC+1:
> 117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
> Rem DNeg, 116
https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/skDAmuwmBwAJ
The last step is to show that, from these already proved two theorems:
> Theorem "Specialization to r"
> 53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r =>
> [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
> Rem DNeg, 52
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/w-98GSofBwAJ
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47 UTC+1:
> Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds or blues"
> | [x=b & z=b | x=r & z=r]
> | [y=b & z=b | y=r & z=r]
> => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
> | [x=r & z=r | x=b & z=b]
> | [y=r & z=r | y=b & z=b]]]
> Conclusion, 3
> | [y=r & z=r | y=b & z=b]]]
https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
We can deduce:
Theorem "Specialization to b"
ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b =>
[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
This is left as an exercise. If would the follow what
x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
is used in the first proof.
Easy, isn't it?
Ross A. Finlayson
Nov 27, 2022, 8:56:21 AM11/27/22
to
the objects, still keeps all the previous possible derivations in place for
the following derivations. (The, "generality".)
I have zero or no interest in writing in your tool, per se.
Have you heard of Russell's types? It's "types" in "sets".
Have you ever read a text on type theory?
It's very fundamental these days for programming in computer science.
(Type theory.)
Mostowski Collapse
Nov 27, 2022, 10:53:05 AM11/27/22
to
Rossy Boys amazing jet lag. After like two weeks he starts thinking
about the problem. So there is still hope, Rossy Boy has a brain cell?
Hint: Its a very simple special case of Ramsey, if we look at vertex color:
Every blue red triangle contains an unicolored edge.
https://en.wikipedia.org/wiki/Ramsey_theory
about the problem. So there is still hope, Rossy Boy has a brain cell?
Hint: Its a very simple special case of Ramsey, if we look at vertex color:
Every blue red triangle contains an unicolored edge.
https://en.wikipedia.org/wiki/Ramsey_theory
Ross A. Finlayson
Nov 27, 2022, 11:03:13 AM11/27/22
to
Wie gehts, troll, mann kann nicht aber daruber.
Mostowski Collapse
Nov 27, 2022, 11:07:04 AM11/27/22
to
The Ramsey reading could allow to explain this formula:
> Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
First the triangle, blue red:
> / \
> / \
> / \
> / \
> y---------z
Then one edge unicolored:
> /
> /
> /
> /
> y
Then another edge unicolored :
> \
> \
> \
> \
> z
Then last edge unicolored :
Amazing that this is so difficult for Wonky Man.
(And I guess also a big hurdle for Rossy Boy)
LMAO!
> Theorem: "3 objects either red or blue" => "2 out of 3 all reds or blues"
> ALL(x):ALL(y):ALL(y):ALL(r):ALL(b):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
[x=r | x=b] & [y=r | y=b] & [z=r | z=b]
> x
> / \
> / \
> / \
> / \
> y---------z
Then one edge unicolored:
x=r & y=r | x=b & y=b
> x
> /
> /
> /
> /
> y
Then another edge unicolored :
[x=r & z=r | x=b & z=b]
> x
> \
> \
> \
> \
> z
Then last edge unicolored :
[x=r & z=r | x=b & z=b]
>
>
>
>
>
> y---------z
>
>
>
>
>
Amazing that this is so difficult for Wonky Man.
(And I guess also a big hurdle for Rossy Boy)
LMAO!
Coke Alfero
Nov 27, 2022, 11:44:44 AM11/27/22
to
Mostowski Collapse wrote:
> Mostowski Collapse schrieb am Samstag, 26. November 2022 um 16:50:16
> UTC+1:
>> 117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
>> Rem DNeg, 116
watch this modrefaka khazar sondre bitch. Just not saying he is stupid.
> Mostowski Collapse schrieb am Samstag, 26. November 2022 um 16:50:16
> UTC+1:
>> 117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
>> Rem DNeg, 116
Watch the imbecile, how "serious" he is supposed to be.
the khazar is "serious", not fucking stupid.
‘Hard times’ ahead for Europe – NATO
Backing Ukraine is causing living costs to soar, the bloc's chief Jens
Stoltenberg admitted
https://rt.com/news/567269-hard-times-europe-ukraine-stoltenberg/
Dan Christensen
Nov 27, 2022, 12:34:32 PM11/27/22
to
On Sunday, November 27, 2022 at 5:26:26 AM UTC-5, Mostowski Collapse wrote:
> Yeah, you missed it. I have completed the proof. See here:
>
You may perhaps completed an alternative (and longer) proof, but which part do you imagine is a statement, proof and application of the required WLOG principle. See examples of such statements at https://www.cl.cam.ac.uk/~jrh13/papers/wlog.pdf
> Yeah, you missed it. I have completed the proof. See here:
>
> Mostowski Collapse schrieb am Samstag, 26. November 2022 um 16:50:16 UTC+1:
> > 117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
Compare to my conclusion (with no "shortcuts")
97. EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
Cases, 19, 96
> > Rem DNeg, 116
117 lines? THIS is your "shortcut???" Why bother?
Mostowski Collapse
Nov 27, 2022, 3:30:04 PM11/27/22
to
It was repeated to you a 1000-times, see below. Whats
is so difficult to understand moron? This post is
already almost a week old, meanwhile I did all proofs
with DC Poop, and verified my claim.
Whats wrong with you? Are you drunk?
Mostowski Collapse schrieb am Mittwoch, 23. November 2022 um 21:30:37 UTC+1:
> Thats rather easy, the Galois connection is a permutation, of the colors.
> The only non-identity permutation of two colors is swapping them.
>
> So lets write the desired theorem with the colors as additional
> parameters, namely:
>
> C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
> => ((x=red & y=red) v (x=blue & y=blue) v
> (y=red & z=red) v (y=blue & z=blue) v
> (x=red & z=red) v (x=blue & z=blue)))
>
> Now you prove:
>
> ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
> ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
>
> Then you can conclude:
>
> ALL(red):ALL(blue):(x=blue => C(red,blue,x,y,z))
>
> Here my claim verified by Wolfgang Schwartz tool:
>
> (∀r∀b(x=r → Crbxyz) ∧ ∀r∀b(Crbxyz → Cbrxyz)) → ∀r∀b(x=b → Crbxyz) is valid.
> https://www.umsu.de/trees/#~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~1~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6r~6b%28x=b~5C%28r,b,x,y,z%29%29
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/P_feO3tKBgAJ
is so difficult to understand moron? This post is
already almost a week old, meanwhile I did all proofs
with DC Poop, and verified my claim.
Whats wrong with you? Are you drunk?
Mostowski Collapse schrieb am Mittwoch, 23. November 2022 um 21:30:37 UTC+1:
> Thats rather easy, the Galois connection is a permutation, of the colors.
> The only non-identity permutation of two colors is swapping them.
>
> So lets write the desired theorem with the colors as additional
> parameters, namely:
>
> C(red, blue,x,y,z) <=> ((x=red & y=red & z=red) v (x=blue & y=blue & z=blue)
> => ((x=red & y=red) v (x=blue & y=blue) v
> (y=red & z=red) v (y=blue & z=blue) v
> (x=red & z=red) v (x=blue & z=blue)))
>
> Now you prove:
>
> ALL(red):ALL(blue):(x=red => C(red,blue,x,y,z))
> ALL(red):ALL(blue):(C(red,blue,x,y,z) => C(blue,red,x,y,z))
>
> Then you can conclude:
>
> ALL(red):ALL(blue):(x=blue => C(red,blue,x,y,z))
>
> Here my claim verified by Wolfgang Schwartz tool:
>
> (∀r∀b(x=r → Crbxyz) ∧ ∀r∀b(Crbxyz → Cbrxyz)) → ∀r∀b(x=b → Crbxyz) is valid.
> https://www.umsu.de/trees/#~6r~6b%28x=r~5C%28r,b,x,y,z%29%29~1~6r~6b%28C%28r,b,x,y,z%29~5C%28b,r,x,y,z%29%29~5~6r~6b%28x=b~5C%28r,b,x,y,z%29%29
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/P_feO3tKBgAJ
Mostowski Collapse
Nov 27, 2022, 3:36:58 PM11/27/22
to
You are a fucking liar, again and again.
What part of WLOG don't you understand moron?
If you only need to prove x=a, and x=b follows,
Isnt this a WLOG principle?
It is what you failed to archive:
I have been unable to formally justify the
without-loss-of-generality claim.
https://www.dcproof.com/WithoutLossOfGenerality.htm
And it is what I managed to do:
> Theorem "Specialization to r"
> 53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r =>
or blues"
> | [x=b & z=b | x=r & z=r]
> | [y=b & z=b | y=r & z=r]
> => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
Mostowski Collapse schrieb am Sonntag, 27. November 2022 um 12:19:06 UTC+1:
> Theorem specialize to b
> 37 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b =>
https://groups.google.com/g/sci.math/c/R9cC3p0ooCI/m/5BIB87RmBwAJ
So get lost you blistering imbecil.
What part of WLOG don't you understand moron?
If you only need to prove x=a, and x=b follows,
Isnt this a WLOG principle?
It is what you failed to archive:
I have been unable to formally justify the
without-loss-of-generality claim.
And it is what I managed to do:
> Theorem "Specialization to r"
> 53 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r =>
> [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b &
z=b]]]
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b &
z=b]]]
> Rem DNeg, 52
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/w-98GSofBwAJ
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47
UTC+1:
> Theorem: Swap "3 objects either red or blue" => "2 out of 3 all reds
https://groups.google.com/g/sci.math/c/S-AyjY4rK7s/m/w-98GSofBwAJ
Mostowski Collapse schrieb am Donnerstag, 24. November 2022 um 18:35:47
UTC+1:
or blues"
> 29 ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=b | x=r] & [y=b | y=r] &
[z=b | z=r] => x=b & y=b | x=r & y=r
> | [x=b & z=b | x=r & z=r]
> | [y=b & z=b | y=r & z=r]
> => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b
> | [x=r & z=r | x=b & z=b]
> | [y=r & z=r | y=b & z=b]]]
> Conclusion, 3
> | [y=r & z=r | y=b & z=b]]]
https://groups.google.com/g/sci.math/c/3vtZ4jfP3Y0/m/7h0dWoWPBgAJ
Mostowski Collapse schrieb am Sonntag, 27. November 2022 um 12:19:06 UTC+1:
> Theorem specialize to b
> 37 ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b =>
> [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] =>
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b &
z=b]]]
> Rem DNeg, 36
> x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b &
z=b]]]
https://groups.google.com/g/sci.math/c/R9cC3p0ooCI/m/5BIB87RmBwAJ
So get lost you blistering imbecil.
Message has been deleted
Dan Christensen
Nov 27, 2022, 10:57:07 PM11/27/22
to
On Sunday, November 27, 2022 at 12:34:32 PM UTC-5, Dan Christensen wrote:
> On Sunday, November 27, 2022 at 5:26:26 AM UTC-5, Mostowski Collapse wrote:
> > Yeah, you missed it. I have completed the proof. See here:
> >
> You may perhaps have completed an alternative (and longer) proof, but which part do you imagine is a statement, proof and application of the required WLOG principle. See examples of such statements at https://www.cl.cam.ac.uk/~jrh13/papers/wlog.pdf
> On Sunday, November 27, 2022 at 5:26:26 AM UTC-5, Mostowski Collapse wrote:
> > Yeah, you missed it. I have completed the proof. See here:
> >
On p. 2 we have an example of the following WLOG theorem:
"For any property P of two real numbers, if the property is symmetric between those two numbers (∀x y. P x y ⇔ P y x) and assuming x ≤ y the property holds (∀x y. x ≤ y ⇒ P x y), then we can conclude that it holds for all real numbers (∀x y. P x y)."
In the notation of DC Proof:
ALL(x):ALL(y):[x in r & y in r => [P(x,y) <=> P(y,x)]]
& ALL(x):ALL(y):[x in r & y in r => [x<=y => P(x,y)]]
=> ALL(x):ALL(y):[x in r & y in r => P(x,y)]
On what line in your proof do you cite such a theorem?
> > Mostowski Collapse schrieb am Samstag, 26. November 2022 um 16:50:16 UTC+1:
> > > 117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
> What are p and q? Elements of some set? Also, you should avoid applying existential specification to conditionals like this. Have you learned nothing from the Drinker's Paradox? EXIST(x):[A(x) => B] is always true regardless of which A and B are used, provided only that EXIST(x):~A(x). A(x) would be quite useless otherwise.
You really need to fix up your conclusion.
Mostowski Collapse
Nov 28, 2022, 7:11:32 AM11/28/22
to
Existentially quantified variables. Why do you ask?
Never seen a formula in logic.
What do you see in the morning when you look into
the mirror? A stupid idiot dickhead?
To the best of my knowledge:
EXIST(x):(A(x) & B(x)) implies EXIST(x):B(x)
So you could also use your:
97 EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
Cases, 19, 96
And then derive:
EXIST(a):EXIST(b):[~a=b & color(a)=color(b)]
If you were not a complete imbecile. But unfortunately
you don´t have a single brain cell.
Never seen a formula in logic.
What do you see in the morning when you look into
the mirror? A stupid idiot dickhead?
To the best of my knowledge:
EXIST(x):(A(x) & B(x)) implies EXIST(x):B(x)
So you could also use your:
97 EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
Cases, 19, 96
And then derive:
EXIST(a):EXIST(b):[~a=b & color(a)=color(b)]
If you were not a complete imbecile. But unfortunately
you don´t have a single brain cell.
Mostowski Collapse
Nov 28, 2022, 8:06:42 AM11/28/22
to
See here, the more simpler theorem:
Mostowski Collapse schrieb am Montag, 28. November 2022 um 14:03:01 UTC+1:
> Ok, that ~u=v & ~u=w & ~v=w wasn´t needed was
> a kind of proof smell, so needed to revise the proof,
>
> in particular a different theorem is now proved.
> Using the lemma, we can prove, now ~u=v & ~u=w & ~v=w
> was used. We find the following conclusion:
>
> 76 EXIST(p):EXIST(q):[~p=q & color(p)=color(q)]
> Rem DNeg, 75
https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/dt4nFvW6BwAJ
You could easily add some axioms u e s, v e s and w e s,
and then prove your variant, but this doesn´t add much.
Mostowski Collapse schrieb am Montag, 28. November 2022 um 14:03:01 UTC+1:
> Ok, that ~u=v & ~u=w & ~v=w wasn´t needed was
> a kind of proof smell, so needed to revise the proof,
>
> in particular a different theorem is now proved.
> Using the lemma, we can prove, now ~u=v & ~u=w & ~v=w
> was used. We find the following conclusion:
>
> 76 EXIST(p):EXIST(q):[~p=q & color(p)=color(q)]
> Rem DNeg, 75
https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/dt4nFvW6BwAJ
You could easily add some axioms u e s, v e s and w e s,
and then prove your variant, but this doesn´t add much.
Dan Christensen
Nov 28, 2022, 12:28:38 PM11/28/22
to
On Monday, November 28, 2022 at 8:06:42 AM UTC-5, Mostowski Collapse wrote:
> See here, the more simpler theorem:
>
> Mostowski Collapse schrieb am Montag, 28. November 2022 um 14:03:01 UTC+1:
> > Ok, that ~u=v & ~u=w & ~v=w wasn´t needed was
> > a kind of proof smell, so needed to revise the proof,
> >
> > in particular a different theorem is now proved.
> > Using the lemma, we can prove, now ~u=v & ~u=w & ~v=w
> > was used. We find the following conclusion:
> >
> > 76 EXIST(p):EXIST(q):[~p=q & color(p)=color(q)]
> > Rem DNeg, 75
> https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/dt4nFvW6BwAJ
>
Your final conclusion was:
> See here, the more simpler theorem:
>
> Mostowski Collapse schrieb am Montag, 28. November 2022 um 14:03:01 UTC+1:
> > Ok, that ~u=v & ~u=w & ~v=w wasn´t needed was
> > a kind of proof smell, so needed to revise the proof,
> >
> > in particular a different theorem is now proved.
> > Using the lemma, we can prove, now ~u=v & ~u=w & ~v=w
> > was used. We find the following conclusion:
> >
> > 76 EXIST(p):EXIST(q):[~p=q & color(p)=color(q)]
> > Rem DNeg, 75
> https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/dt4nFvW6BwAJ
>
117 EXIST(p):EXIST(q):[~p=q => color(p)=color(q)]
> You could easily add some axioms u e s, v e s and w e s,
> and then prove your variant, but this doesn´t add much.
Your final conclusion (above) is of the form EXIST(p):EXIST(q):[~p=q => X]. It would be true no matter what proposition you substituted for X. You could even prove EXIST(p):EXIST(q):[~p=q => ~color(p)=color(q)] (negating the consequent). Not good.
> and then prove your variant, but this doesn´t add much.
Mostowski Collapse
Nov 29, 2022, 1:24:21 PM11/29/22
to
No the final conclusion is now:
> > > 76 EXIST(p):EXIST(q):[~p=q & color(p)=color(q)]
> > > Rem DNeg, 75
> > https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/dt4nFvW6BwAJ
I made a revision.
> > > 76 EXIST(p):EXIST(q):[~p=q & color(p)=color(q)]
> > > Rem DNeg, 75
> > https://groups.google.com/g/sci.math/c/-p0Yr9Ja5io/m/dt4nFvW6BwAJ
Mostowski Collapse
Nov 30, 2022, 5:16:37 PM11/30/22
to
Can you prove this WLOG principle?
* ------------------------------------------------------------------------- *)
(* A "without loss of generality" lemma for symmetry. *)
(* ------------------------------------------------------------------------- *)
∀a∀b(Pa → Cab) ∧
∀a∀b(Cab → Cba) →
∀a∀b(Pb → Cab)
Its the basis for this here, which you could't solve using some WLOG:
"If three objects are each painted either red or blue,
then there must be at least two objects of the same color."
Maybe give it a second try?
LMAO!
Dan Christensen schrieb am Montag, 21. November 2022 um 21:12:04 UTC+1:
> What is meant by "without loss of generality" in a mathematical proof?
>
> "In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
>
> "Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
> --George Bergman
> https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
>
> Here I formally prove the following theorem from Wikipedia:
>
> "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
>
> Wikipeda provides the following INFORMAL proof:
>
> "A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
>
> https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
>
> Formally, I prove (link below):
>
>
> https://www.dcproof.com/WithoutLossOfGenerality.htm (new version)
* ------------------------------------------------------------------------- *)
(* A "without loss of generality" lemma for symmetry. *)
(* ------------------------------------------------------------------------- *)
∀a∀b(Pa → Cab) ∧
∀a∀b(Cab → Cba) →
∀a∀b(Pb → Cab)
Its the basis for this here, which you could't solve using some WLOG:
"If three objects are each painted either red or blue,
then there must be at least two objects of the same color."
LMAO!
Dan Christensen schrieb am Montag, 21. November 2022 um 21:12:04 UTC+1:
> What is meant by "without loss of generality" in a mathematical proof?
>
> "In giving a mathematical proof, if we say that 'without loss of generality' we may assume that some condition X holds, this means that if we can establish the result in the case where X holds, we can deduce from this that it holds in general. After saying this, one usually assumes that X holds for the rest of the proof. [...]
>
> "Of course, whether it is 'clear' that knowing a result in one case implies that it is true in other cases depends on the situation, and on the mathematical background of one's readership."
> --George Bergman
> https://math.berkeley.edu/~gbergman/ug.hndts/sets_etc,t=1.pdf
>
> Here I formally prove the following theorem from Wikipedia:
>
> "If three objects are each painted either red or blue, then there must be at least two objects of the same color."
>
> Wikipeda provides the following INFORMAL proof:
>
> "A proof: Assume, without loss of generality, that the first object is red. If either of the other two objects is red, then we are finished; if not, then the other two objects must both be blue and we are still finished."
>
> https://en.wikipedia.org/wiki/Without_loss_of_generality#Example
>
> Formally, I prove (link below):
>
> EXIST(a):EXIST(b):[a e s & b e s & [~a=b & color(a)=color(b)]]
>
>
> Where
>
> s = a set of 3 distinct elements: {x, y, z}
>
> colors = a set of 2 distinct elements: {red, blue}
>
> color(n) = the color of object n
>
> I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
>
> It seems unlikely that the without-loss-of-generality claim can be justified using the ordinary rules of logic found in most math textbooks as has been used here:
>
> s = a set of 3 distinct elements: {x, y, z}
>
> colors = a set of 2 distinct elements: {red, blue}
>
> color(n) = the color of object n
>
> I have been unable to formally justify the without-loss-of-generality claim. Instead, I first prove the case of the first object being red (lines 33-64), then, the case of it being blue (lines 65-96). The two sub-proofs are only superficially alike (both are 31 lines).
>
>
> https://www.dcproof.com/WithoutLossOfGenerality.htm (new version)
Message has been deleted
Dan Christensen
Nov 30, 2022, 8:46:03 PM11/30/22
to
On Wednesday, November 30, 2022 at 5:16:37 PM UTC-5, Mostowski Collapse wrote:
> Can you prove this WLOG principle?
>
> * ------------------------------------------------------------------------- *)
> (* A "without loss of generality" lemma for symmetry. *)
> (* ------------------------------------------------------------------------- *)
>
> ∀a∀b(Pa → Cab) ∧
> ∀a∀b(Cab → Cba) →
> ∀a∀b(Pb → Cab)
>
How about something a little more conventional with no mysterious, unspecified domain in the background:
> Can you prove this WLOG principle?
>
> * ------------------------------------------------------------------------- *)
> (* A "without loss of generality" lemma for symmetry. *)
> (* ------------------------------------------------------------------------- *)
>
> ∀a∀b(Pa → Cab) ∧
> ∀a∀b(Cab → Cba) →
> ∀a∀b(Pb → Cab)
>
ALL(a):ALL(b):[U(a) & U(b) => [P(a) => C(a,b)]]
& ALL(a):ALL(b):[U(a) & U(b) => [C(a,b) => C(b,a)]]
=> ALL(a):ALL(b):[U(a) & U(b) => [P(b) => C(a,b)]]
> Its the basis for this here, which you could't solve using some WLOG:
> "If three objects are each painted either red or blue,
> then there must be at least two objects of the same color."
0 new messages