Two similar properties with different results

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WM

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Nov 25, 2022, 5:10:00 AM11/25/22
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Every element q of the set ℚ of all rational numbers can be enumerated. In every step n we get another number q_n which has the properties (1) to have an index n and (2) to have ℵo successors which are not enumerated in or before step n.

Now we can conclude that the property (1) is inherited by all elements of the complete set ℚ which therefore may be called a countable set, but although property (2) is also inherited by all elements of the complete set ℚ it must not be called a discountable set, that is a set all elements of which can be subtracted without changing the cardinality of the remainder.

Regards, WM

Archimedes Plutonium

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Nov 25, 2022, 12:41:51 PM11/25/22
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Germany's WM holding back Germany from the truth of math, logic, and physics because of his insane spamming nattering nuttery, going on for the 3rd decade. Why the insane WM believes 2 OR 1 = 3 with AND as subtraction, and he believes slant cut of cone is ellipse when in reality it is a oval. WM is so insane in math he never realized calculus was geometry and never can do a geometry proof of Fundamental Theorem of Calculus, but worst of all, is the insane spamming nutjob WM is too dumb to ask a simple question, which is the Atom's true electron-- Muon or 0.5MeV particle.

On Friday, November 25, 2022 at 4:10:00 AM UTC-6, WM wrote:
> Every element q

Re: Wolfgang Mueckenheim fuck my ass!
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by zelos...@gmail.com Sep 23, 2022, 12:15:59 AM


Re: Wolfgang Mueckenheim math-mindless-fuckdog
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by Kristjan Robam Sep 7, 2022, 3:08:10 AM


Re: My fucking of her corpse
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by zelos...@gmail.com Sep 9, 2022, 1:01:23 AM


Re: Germany's barking fuckdog Wolfgang Mueckenheim WM and his trailing barking fuckdogs Sergi_o, Jim Burns, TheRafters, Fritz Feldhase, Gus Gassmann, Ben Bacarisse, play act SPAMMING of sci.math needs to be kicked out of sci.math
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by Chris M. Thomasson Oct 26, 2022, 10:35:00 PM


Re: -Muck the Puke WM & Gottingen and the whole of Germany cannot admit slant cut of cone is Oval never ellipse, nor can anyone there do a geometry proof of Fundamental Theorem of Calculus-- all they seem to do is "dark numbers bullshit"
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by Jan Sep 16, 2022, 12:28:12 PM

3rd published book

AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.

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Proofs Ellipse is never a Conic section, always a Cylinder section and a Well Defined Oval definition//Student teaches professor series, book 5 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 14May2022. This is AP's 68th published book of science.

Preface: A similar book on single cone cut is a oval, never a ellipse was published in 11Mar2019 as AP's 3rd published book, but Amazon Kindle converted it to pdf file, and since then, I was never able to edit this pdf file, and decided rather than struggle and waste time, decided to leave it frozen as is in pdf format. Any new news or edition of ellipse is never a conic in single cone is now done in this book. The last thing a scientist wants to do is wade and waddle through format, when all a scientist ever wants to do is science itself. So all my new news and thoughts of Conic Sections is carried out in this 68th book of AP. And believe you me, I have plenty of new news.

In the course of 2019 through 2022, I have had to explain this proof often on Usenet, sci.math and sci.physics. And one thing that constant explaining does for a mind of science, is reduce the proof to its stripped down minimum format, to bare bones skeleton proof. I can prove the slant cut in single cone is a Oval, never the ellipse in just a one sentence proof. Proof-- A single cone and oval have just one axis of symmetry, while a ellipse requires 2 axes of symmetry, hence slant cut is always a oval, never the ellipse.

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#12-2, 11th published book

World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 15Dec2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.

Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". And very surprising that most math professors cannot tell the difference between a "proving something" and that of "analyzing something". As if an analysis is the same as a proof. We often analyze various things each and every day, but few if none of us consider a analysis as a proof. Yet that is what happened in the science of mathematics where they took an analysis and elevated it to the stature of being a proof, when it was never a proof.

To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.


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My 5th published book

Suspend all College Classes in Logic, until they Fix their Errors // Teaching True Logic series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 29Mar2021. This is AP's 5th published book of science.
Preface:
First comes Logic-- think straight and clear which many logic and math professors are deaf dumb and blind to, and simply refuse to recognize and fix their errors.

The single biggest error of Old Logic of Boole and Jevons was their "AND" and "OR" connectors. They got them mixed up and turned around. For their logic ends up being that of 3 OR 2 = 5 with 3 AND 2 = either 3 or 2 but never 5, when even the local village idiot knows that 3 AND 2 = 5 (addition) with 3 OR 2 = either 3 or 2 (subtraction). The AND connector in Logic stems from the idea, the mechanism involved, that given a series of statements, if just one of those many statements has a true truth value, then the entire string of statements is overall true, and thus AND truth table is truly TTTF and never TFFF. And secondly, their error of the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability end conclusion.

My corrections of Old Logic have a history that dates before 1993, sometime around 1991, I realized the Euclid proof of infinitude of primes was illogical, sadly sadly wrong, in that the newly formed number by "multiply the lot and add 1" was necessarily a new prime in the indirect proof method. So that my history of fixing Old Logic starts in 1991, but comes to a synthesis of correcting all four of the connectors of Equal/not, And, Or, If->Then, by 2015.

Cover picture: some may complain my covers are less in quality, but I have a good reason for those covers-- I would like covers of math or logic to show the teacher's own handwriting as if he were back in the classroom writing on the blackboard or an overhead projector.

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137th published book

Introduction to AP's TEACHING TRUE PHYSICS// Physics textbook series, book 1 Kindle Edition
by Archimedes Plutonium (Author)



#1 New Release in Electromagnetic Theory

This will be AP's 137th published book on science. And the number 137 is special to me for it is the number of QED, Quantum Electrodynamics as the inverse fine structure constant. I can always remember 137 as that special constant of physics and so I can remember where Teaching True Physics was started by me.

Time has come for the world to have the authoritative textbooks for all of High School and College education. Written by the leading physics expert of the time. The last such was Feynman in the 1960s with Feynman Lectures on Physics. The time before was Maxwell in 1860s with his books and Encyclopedia Britannica editorship. The time is ripe in 2020 for the new authoritative texts on physics. It will be started in 2020 which is 60 years after Feynman. In the future, I request the physics community updates the premier physics textbook series at least every 30 years. For we can see that pattern of 30 years approximately from Faraday in 1830 to Maxwell in 1860 to Planck and Rutherford in about 1900, to Dirac in 1930 to Feynman in 1960 and finally to AP in 1990 and 2020. So much happens in physics after 30 years, that we need the revisions to take place in a timely manner. But also, as we move to Internet publishing such as Amazon's Kindle, we can see that updates can take place very fast, as editing can be a ongoing monthly or yearly activity. I for one keep constantly updating all my published books, at least I try to.

Feynman was the best to make the last authoritative textbook series for his concentration was QED, Quantum Electrodynamics, the pinnacle peak of physics during the 20th century. Of course the Atom Totality theory took over after 1990 and all of physics; for all sciences are under the Atom Totality theory.
And as QED was the pinnacle peak before 1990, the new pinnacle peak is the Atom Totality theory. The Atom Totality theory is the advancement of QED, for the Atom Totality theory primal axiom says -- All is Atom, and atoms are nothing but Electricity and Magnetism.
Length: 64 pages

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#2-2, 145th published book


TEACHING TRUE PHYSICS//Junior High School// Physics textbook series, book 2
Kindle Edition
by Archimedes Plutonium (Author)

What I am doing is clearing the field of physics, clearing it of all the silly mistakes and errors and beliefs that clutter up physics. Clearing it of its fraud and fakeries and con-artistry. I thought of doing these textbooks starting with Senior year High School, wherein I myself started learning physics. But because of so much fraud and fakery in physics education, I believe we have to drop down to Junior year High School to make a drastic and dramatic emphasis on fakery and con-artistry that so much pervades science and physics in particular. So that we have two years in High School to learn physics. And discard the nonsense of physics brainwash that Old Physics filled the halls and corridors of education.

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• Print length : 78 pages
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• Best Sellers Rank: #185,995 in Kindle Store (See Top 100 in Kindle Store)
◦ #42 in Two-Hour Science & Math Short Reads
◦ #344 in Physics (Kindle Store)
◦ #2,160 in Physics (Books)




#2-3, 146th published book

TEACHING TRUE PHYSICS// Senior High School// Physics textbook series, book 3
Kindle Edition
by Archimedes Plutonium (Author)

I believe that in knowing the history of a science is knowing half of that science. And that if you are amiss of knowing the history behind a science, you have only a partial understanding of the concepts and ideas behind the science. I further believe it is easier to teach a science by teaching its history than any other means of teaching. So for senior year High School, I believe physics history is the best way of teaching physics. And in later years of physics courses, we can always pick up on details. So I devote this senior year High School physics to a history of physics, but only true physics. And there are few books written on the history of physics, so I chose Asimov's The History of Physics, 1966 as the template book for this textbook. Now Asimov's book is full of error and mistakes, and that is disappointing but all of Old Physics is full of error. On errors and mistakes of Old Physics, the best I can do is warn the students, and the largest warning of all is that whenever someone in Old Physics says "electron" what they are talking about is really the Dirac magnetic monopole. And whenever they talk about the Rutherford-Bohr model of the atom, they are talking about huge huge grave mistakes, for the true atom is protons as 8 ringed toruses with a muon stuck inside of a proton doing the Faraday law and producing those magnetic monopoles as electricity. I use Asimov's book as a template but in the future, I hope to rewrite this textbook using no template at all, that is if I have time in the future.
Cover Picture: Is the book The History of Physics, by Isaac Asimov, 1966 and on top of the book are 4 cut-outs of bent circles representing magnetic monopoles which revolutionizes modern physics, especially the ElectroMagnetic theory.

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#2-4, 151st published book

TEACHING TRUE PHYSICS// 1st year College// Physics textbook series, book 4
Kindle Edition
by Archimedes Plutonium (Author)

Preface: This is AP's 151st book of science published. It is one of my most important books of science because 1st year college physics is so impressionable on students, if they should continue with physics, or look elsewhere for a career. And also, physics is a crossroad to all the other hard core sciences, where physics course is mandatory such as in chemistry or even biology. I have endeavored to make physics 1st year college to be as easy and simple to learn. In this endeavor to make physics super easy, I have made the writing such that you will see core ideas in all capital letters as single sentences as a educational tool. And I have made this textbook chapter writing follow a logical pattern of both algebra and geometry concepts, throughout. The utmost importance of logic in physics needs to be seen and understood. For I have never seen a physics book, prior to this one that is logical. Every Old Physics textbook I have seen is scatter-brained in topics and in writing. I use as template book of Halliday & Resnick because a edition of H&R was one I was taught physics at University of Cincinnati in 1969. And in 1969, I had a choice of majors, do I major in geology, or mathematics, or in physics, for I will graduate from UC in 1972. For me, geology was too easy, but physics was too tough, so I ended up majoring in mathematics. If I had been taught in 1969 using this textbook that I have written, I would have ended up majoring in physics, my first love. For physics is not hard, not hard at all, once you clear out the mistakes and the obnoxious worthless mathematics that clutters up Old Physics, and the illogic that smothers much of Old Physics.

Maybe it was good that I had those impressions of physics education of poor education, which still exists throughout physics today. Because maybe I am forced to write this book, because of that awful experience of learning physics in 1969. Without that awful experience, maybe this textbook would have never been written by me.

Cover picture is the template book of Halliday & Resnick, 1988, 3rd edition Fundamentals of Physics and sitting on top are cut outs of "half bent circles, bent at 90 degrees" to imitate magnetic monopoles. Magnetic Monopoles revolutionizes physics education, and separates-out, what is Old Physics from what is New Physics.

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Sergi o

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Nov 25, 2022, 1:13:08 PM11/25/22
to
the above is nonsense. your consistent mistake is that you stop at n in an infinite set, and declare the rest are unknown. Fail.

Ben Bacarisse

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Nov 25, 2022, 4:15:25 PM11/25/22
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WM <askas...@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

> Every element q of the set ℚ of all rational numbers can be
> enumerated.

Here's a (remarkably simple) successor function for Q+:

S(q) = 1 / (2[q] - q + 1) ([x] is the floor function)

> In every step n we get another number q_n which has the properties (1)
> to have an index n and (2) to have ℵo successors which are not
> enumerated in or before step n.

q_1 = 1, q_2 = S(q_1) = S(1), q_3 = S(q_2) = S(S(1)), ...

> Now we can conclude that the property (1) is inherited by all elements
> of the complete set ℚ which therefore may be called a countable set,

The property is not "inherited". For every q in Q+ there is an n such
that S^n(1) = q.

> but although property (2) is also inherited by all elements of the
> complete set ℚ it must not be called a discountable set, that is a set
> all elements of which can be subtracted without changing the
> cardinality of the remainder.

There is no set with this property. If all elements of a set X are
subtracted from X, the result has cardinality 0: X \ X = {}. However,
for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
all elements of Q+ being subtracted.

You need to find a more vague wording if you are to bamboozle your
students this way.

I suspect all this is true in WMaths as well, but you once told me that
you can not yet define set membership, equality and difference in WMaths
so maybe it isn't. Any progress on that yet, by the way? I'd love to
know the definitions so I can attempt to prove the one great theorem of
WMaths: the existence of sets X and Y with Y ∈ X and X \ {Y} = X.

--
Ben.

WM

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Nov 26, 2022, 5:16:22 AM11/26/22
to
Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
> WM <askas...@gmail.com> writes:

> > but although property (2) is also inherited by all elements of the
> > complete set ℚ it must not be called a discountable set, that is a set
> > all elements of which can be subtracted without changing the
> > cardinality of the remainder.

> There is no set with this property.

If you subtract individually definable elements, then almost all will remain.

> If all elements of a set X are
> subtracted from X, the result has cardinality 0: X \ X = {}.

Here we are talking about individually definable subtractions as we should talk about individually definable mappings.

> However,
> for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
> all elements of Q+ being subtracted.

That is a proof that never all can be subtracted individually.
>
> You need to find a more vague wording if you are to bamboozle your
> students this way.

They can think. That lowers the chances of you claim. In my proof using the meanwhile well-known matrices, I show that in no definable step any O leaves, that means that not even one more fraction is indexed than at the start. The claim that "in the limit" all are indexed neveretheless is hardly acceptable.

Regards, WM

FromTheRafters

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Nov 26, 2022, 11:11:23 AM11/26/22
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WM formulated on Saturday :
> Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
>> WM <askas...@gmail.com> writes:
>
>>> but although property (2) is also inherited by all elements of the
>>> complete set ℚ it must not be called a discountable set, that is a set
>>> all elements of which can be subtracted without changing the
>>> cardinality of the remainder.
>
>> There is no set with this property.
>
> If you subtract individually definable elements, then almost all will remain.

Silly man, if they (the left behind) were not definable then they
wouldn't have been granted inclusion in the set in the first place. A
set is a collection of well defined objects.

=================================================
1. SETS
Definition: In mathematics, a well-defined collection of distinct
objects is called a set.
=================================================


https://acikders.ankara.edu.tr/pluginfile.php/64620/mod_resource/content/0/1.%20Sets.pdf

Sergi o

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Nov 26, 2022, 11:13:13 AM11/26/22
to
On 11/26/2022 4:16 AM, WM wrote:
> Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
>> WM <askas...@gmail.com> writes:
>
>>> but although property (2) is also inherited by all elements of the
>>> complete set ℚ it must not be called a discountable set, that is a set
>>> all elements of which can be subtracted without changing the
>>> cardinality of the remainder.
>
>> There is no set with this property.
>
> If you subtract individually definable *FINITE* elements, then almost all will remain.
>
>> If all elements of a set X are
>> subtracted from X, the result has cardinality 0: X \ X = {}.
>
> Here we are talking about individually definable *FINITE* subtractions as we should talk about individually definable *FINITE* mappings.
>
>> However,
>> for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
>> all elements of Q+ being subtracted.
>
> That is a proof that never all can be subtracted *FINITE* individually.
>>
>> You need to find a more vague wording if you are to bamboozle your
>> students this way.
>

if you are saying this stuff to students, you should be fired, and pay the college back your pay.

>
> Regards, WM

Sergi o

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Nov 27, 2022, 12:50:00 PM11/27/22
to
On 11/25/2022 4:09 AM, WM wrote:
>
> Every element q of the set ℚ of all rational numbers can be enumerated. In every step n we get another number q_n which has the properties (1) to have an index n and (2) to have ℵo successors which are not enumerated in or before step n.

so, WM as ticket master, gives a ticket with a natural number on it to each element q as they enter the gate with each ticket number in sequential
order. Currently WM is at n and has stopped.

Property 1 is a redundant statement.
Property 2 is part of the problem statement, and says WM has stopped at n.

>
> Now we can conclude that the property (1) is inherited by all elements of the complete set ℚ which therefore may be called a countable set,

inherited is the wrong word.
and WM was counting each element q that he gave a ticket to, which also has the count on it, a natural number, counting like counting sheeps.


> but although property (2) is also inherited by all elements of the complete set ℚ

Wrong. All elements are not involved, WM stopped at n. your slight of hand in verbiage change is dishonest.

plonk the rest since an error was made.

>
> Regards, WM

Gus Gassmann

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Nov 27, 2022, 5:19:54 PM11/27/22
to
On Sunday, 27 November 2022 at 13:50:00 UTC-4, Sergi o wrote:
> On 11/25/2022 4:09 AM, WM wrote:
> >
> > Every element q of the set ℚ of all rational numbers can be enumerated. In every step n we get another number q_n which has the properties (1) to have an index n and (2) to have ℵo successors which are not enumerated in or before step n.
> so, WM as ticket master, gives a ticket with a natural number on it to each element q as they enter the gate with each ticket number in sequential
> order.

Correct. A number is only a number if WM says it is.

FromTheRafters

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Nov 28, 2022, 6:34:13 AM11/28/22
to
on 11/27/2022, Gus Gassmann supposed :
Sure, by the Axiom of Because I Said So.

To avoid ambiguity we should also call them "distinguished numbers" and
to avoid confusion of terms we should also call them "definable" or
"attainable numbers" depending upon our mood.

If it is still too clear, see Sergi o's revised and updated "ant list"
for even more fuzzy terminology ideas.

Ben Bacarisse

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Nov 28, 2022, 4:33:23 PM11/28/22
to
WM <askas...@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

> Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
>> WM <askas...@gmail.com> writes:
>
>> > but although property (2) is also inherited by all elements of the
>> > complete set ℚ it must not be called a discountable set, that is a set
>> > all elements of which can be subtracted without changing the
>> > cardinality of the remainder.
>
>> There is no set with this property.
>
> If you subtract individually definable elements, then almost all will
> remain.

Can you write that using mathematics?

>> If all elements of a set X are
>> subtracted from X, the result has cardinality 0: X \ X = {}.
>
> Here we are talking about individually definable subtractions as we
> should talk about individually definable mappings.

You talked about subtracting all elements. You gave no mystery words to
hide what you meant ("individual", "definable", "mappings").

>> However,
>> for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
>> all elements of Q+ being subtracted.
>
> That is a proof that never all can be subtracted individually.

So this is not subtracting all elements of Q. We agree on that.

>> You need to find a more vague wording if you are to bamboozle your
>> students this way.
>
> They can think.

Yet none ever suggested that, in relation to Q, "all elements of which"
means all elements of Q? And when you said "Oh, I mean subtracting any
finite subset" not one student called you out and said "that's not
subtracting all elements"? Sad.

Still not brave enough to say if you have finally managed to define even
the most basic set operations in WMaths, I see. That's because you
can't see any way to do that without backtracking on the One Great
Theorem of WMaths: the existence of sets X and Y with Y ∈ X and, here
comes the surprise, X \ {Y} = X. No doubt you will cut this again...

--
Ben.

WM

unread,
Nov 29, 2022, 12:18:16 PM11/29/22
to
Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
> > Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
> >> WM <askas...@gmail.com> writes:
> >
> >> > but although property (2) is also inherited by all elements of the
> >> > complete set ℚ it must not be called a discountable set, that is a set
> >> > all elements of which can be subtracted without changing the
> >> > cardinality of the remainder.
> >
> >> There is no set with this property.
> >
> > If you subtract individually definable elements, then almost all will
> > remain.
> Can you write that using mathematics?

∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

A natural number is dfinable, if it has a FISON or if you can stop at it when counting to infinity.

> > Here we are talking about individually definable subtractions as we
> > should talk about individually definable mappings.
> You talked about subtracting all elements. You gave no mystery words to
> hide what you meant ("individual", "definable", "mappings").

To subtract an element involves that it can be subtracted as an individual.

> >> However,
> >> for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
> >> all elements of Q+ being subtracted.
> >
> > That is a proof that never all can be subtracted individually.
> So this is not subtracting all elements of Q. We agree on that.

It is impossible to subtract all elements individually.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
Only the whole set can be subtracted with nothing remaining
|ℕ \ {1, 2, 3, ...}| = 0 .

> One Great
> Theorem of WMaths: the existence of sets X and Y with Y ∈ X and, here
> comes the surprise, X \ {Y} = X.

In potential infinity the sets, or better collections, are not static.
With n also n^n^n^n^n belongs to ℕ, but ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

Regards, WM

zelos...@gmail.com

unread,
Nov 29, 2022, 1:03:15 PM11/29/22
to
tisdag 29 november 2022 kl. 18:18:16 UTC+1 skrev WM:
> Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
> > WM <askas...@gmail.com> writes:
> > (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> > Unendlichen" at Hochschule Augsburg.)
> > > Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
> > >> WM <askas...@gmail.com> writes:
> > >
> > >> > but although property (2) is also inherited by all elements of the
> > >> > complete set ℚ it must not be called a discountable set, that is a set
> > >> > all elements of which can be subtracted without changing the
> > >> > cardinality of the remainder.
> > >
> > >> There is no set with this property.
> > >
> > > If you subtract individually definable elements, then almost all will
> > > remain.
> > Can you write that using mathematics?
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>
> A natural number is dfinable, if it has a FISON or if you can stop at it when counting to infinity.

Which is EVERY FUCKING NATURAL NUMBER!

> > > Here we are talking about individually definable subtractions as we
> > > should talk about individually definable mappings.
> > You talked about subtracting all elements. You gave no mystery words to
> > hide what you meant ("individual", "definable", "mappings").
> To subtract an element involves that it can be subtracted as an individual.
> > >> However,
> > >> for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
> > >> all elements of Q+ being subtracted.
> > >
> > > That is a proof that never all can be subtracted individually.
> > So this is not subtracting all elements of Q. We agree on that.
> It is impossible to subtract all elements individually.

What the fuck does "individually" mean?

> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> Only the whole set can be subtracted with nothing remaining
> |ℕ \ {1, 2, 3, ...}| = 0 .

which is meaningless because A\A={} for any set

WM

unread,
Nov 29, 2022, 2:18:44 PM11/29/22
to
zelos...@gmail.com schrieb am Dienstag, 29. November 2022 um 19:03:15 UTC+1:
> tisdag 29 november 2022 kl. 18:18:16 UTC+1 skrev WM:
> > Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
> > > WM <askas...@gmail.com> writes:
> > > (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> > > Unendlichen" at Hochschule Augsburg.)
> > > > Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
> > > >> WM <askas...@gmail.com> writes:
> > > >
> > > >> > but although property (2) is also inherited by all elements of the
> > > >> > complete set ℚ it must not be called a discountable set, that is a set
> > > >> > all elements of which can be subtracted without changing the
> > > >> > cardinality of the remainder.
> > > >
> > > >> There is no set with this property.
> > > >
> > > > If you subtract individually definable elements, then almost all will
> > > > remain.
> > > Can you write that using mathematics?
> > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> >
> > A natural number is definable, if it has a FISON or if you can stop at it when counting to infinity.
> Which is EVERY FUCKING NATURAL NUMBER!

Not those natural numbers which reduce the number of |ℕ|*(|ℕ|-1) not indxed fractions.

> > It is impossible to subtract all elements individually.
> What the fuck does "individually" mean?

It does not reduce the number of |ℕ|*(|ℕ|-1) not indxed fractions.

> > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > Only the whole set can be subtracted with nothing remaining
> > |ℕ \ {1, 2, 3, ...}| = 0 .
> which is meaningless because A\A={} for any set

Not for the definable elements of infinite sets however.

Regards, WM

Sergi o

unread,
Nov 29, 2022, 6:00:02 PM11/29/22
to
On 11/29/2022 11:18 AM, WM wrote:
> Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
>> WM <askas...@gmail.com> writes:
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>> Unendlichen" at Hochschule Augsburg.)
>>> Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
>>>> WM <askas...@gmail.com> writes:
>>>
>>>>> but although property (2) is also inherited by all elements of the
>>>>> complete set ℚ it must not be called a discountable set, that is a set
>>>>> all elements of which can be subtracted without changing the
>>>>> cardinality of the remainder.
>>>
>>>> There is no set with this property.
>>>
>>> If you subtract individually definable elements, then almost all will
>>> remain.
>> Can you write that using mathematics?
>
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>
> A natural number is dfinable, if it has a FISON or if you can stop at it when counting to infinity.

Simple Proof that all natural numbers are "WMs definable"
show a natural number which does not have a FISON.
there are none,
therefore all natural numbers are "WMs definable."

which number you cannot stop at when you are counting to infinity ?
cant name any ? then all natural numbers are "WMs definable"

>
>>> Here we are talking about individually definable subtractions as we
>>> should talk about individually definable mappings.
>> You talked about subtracting all elements. You gave no mystery words to
>> hide what you meant ("individual", "definable", "mappings").
>
> To subtract an element involves that it can be subtracted as an individual.

WMs mystery word "individual"

>
>>>> However,
>>>> for all n |Q+ \ {1, S(1), S(S(1), ..., S^n(1)}| = ℵ0, but in no case are
>>>> all elements of Q+ being subtracted.
>>>
>>> That is a proof that never all can be subtracted individually.
>> So this is not subtracting all elements of Q. We agree on that.
>
> It is impossible to subtract all elements individually.

WMs mystery word "individually"

> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> Only the whole set can be subtracted with nothing remaining
> |ℕ \ {1, 2, 3, ...}| = 0 .
>
>> One Great
>> Theorem of WMaths: the existence of sets X and Y with Y ∈ X and, here
>> comes the surprise, X \ {Y} = X.
>
> In potential infinity the sets, or better collections, are not static.

WMs mystery word "potential infinity"

Sergi o

unread,
Nov 29, 2022, 8:53:29 PM11/29/22
to
a BOT for sure!

Ben Bacarisse

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Nov 29, 2022, 9:32:13 PM11/29/22
to
So A \ A might sometimes be {} and sometimes not. I can see why no one
else is interested in WMaths, and I can see why you can't even define
"collection" membership, equality and difference. How can you establish
any facts at all without defining these basics? Asserting that Y ∈ X
and X \ {Y} = X. is crazy enough, but it's insane to assert it before
you can define membership equality and difference.

Do you, honestly, stand in front of serious minded-students and tell
them that even though you can't define set (or collection) membership,
equality and difference you will be telling them everyone else is wrong
about sets?

--
Ben.

Chris M. Thomasson

unread,
Nov 29, 2022, 11:13:06 PM11/29/22
to
On 11/25/2022 2:09 AM, WM wrote:
>
> Every element q of the set ℚ of all rational numbers can be enumerated. In every step n we get another number q_n which has the properties (1) to have an index n and (2) to have ℵo successors which are not enumerated in or before step n.
>
> Now we can conclude that the property (1) is inherited by all elements of the complete set ℚ which therefore may be called a countable set, but although property (2) is also inherited by all elements of the complete set ℚ it must not be called a discountable set, that is a set all elements of which can be subtracted without changing the cardinality of the remainder.

I am not even sure _you_ can get all of the pairings wrt Cantor Pairing.
What is the pair at index 42?

zelos...@gmail.com

unread,
Nov 30, 2022, 12:51:31 AM11/30/22
to
tisdag 29 november 2022 kl. 20:18:44 UTC+1 skrev WM:
> zelos...@gmail.com schrieb am Dienstag, 29. November 2022 um 19:03:15 UTC+1:
> > tisdag 29 november 2022 kl. 18:18:16 UTC+1 skrev WM:
> > > Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
> > > > WM <askas...@gmail.com> writes:
> > > > (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> > > > Unendlichen" at Hochschule Augsburg.)
> > > > > Ben Bacarisse schrieb am Freitag, 25. November 2022 um 22:15:25 UTC+1:
> > > > >> WM <askas...@gmail.com> writes:
> > > > >
> > > > >> > but although property (2) is also inherited by all elements of the
> > > > >> > complete set ℚ it must not be called a discountable set, that is a set
> > > > >> > all elements of which can be subtracted without changing the
> > > > >> > cardinality of the remainder.
> > > > >
> > > > >> There is no set with this property.
> > > > >
> > > > > If you subtract individually definable elements, then almost all will
> > > > > remain.
> > > > Can you write that using mathematics?
> > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > >
> > > A natural number is definable, if it has a FISON or if you can stop at it when counting to infinity.
> > Which is EVERY FUCKING NATURAL NUMBER!
> Not those natural numbers which reduce the number of |ℕ|*(|ℕ|-1) not indxed fractions.

It is LITERALLY ALL natural numbers, no exception.

> > > It is impossible to subtract all elements individually.
> > What the fuck does "individually" mean?
> It does not reduce the number of |ℕ|*(|ℕ|-1) not indxed fractions.

What the fuck does that mean?

> > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > > Only the whole set can be subtracted with nothing remaining
> > > |ℕ \ {1, 2, 3, ...}| = 0 .
> > which is meaningless because A\A={} for any set
> Not for the definable elements of infinite sets however.

FOR ALL SETS! It is a UNIVERSAL PROPERTY! NO EXCEPTIONS YOU RETARD!

>
> Regards, WM

WM

unread,
Nov 30, 2022, 6:09:11 AM11/30/22
to
Ben Bacarisse schrieb am Mittwoch, 30. November 2022 um 03:32:13 UTC+1:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
>
> > Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
>
> >> One Great
> >> Theorem of WMaths: the existence of sets X and Y with Y ∈ X and, here
> >> comes the surprise, X \ {Y} = X.
> >
> > In potential infinity the sets, or better collections, are not static.
> So A \ A might sometimes be {} and sometimes not.

In potential infinity infinite collections change.

There was no objection to a 'potential infinity' in the form of an unending process, but an 'actual infinity' in the form of a completed infinite set was harder to accept." [H.B. Enderton: "Elements of set theory", Academic Press, New York (1977) p. 14f]

The world of my thoughts, i.e., the collection S of all things which can be objects of my thinking, is infinite. For, if s is an element of S, then the thought s' that s can be an object of my thinking is itself an object of my thinking." [R. Dedekind: "Was sind und was sollen die Zahlen?", 8th ed., Vieweg, Braunschweig (1960) p. 14] This is potential infinity too, because never more than a finite number of thoughts can have been thought.

"In spite of significant difference between the notions of the potential and actual infinite, where the former is a variable finite magnitude, growing above all limits," [Cantor, p. 374]

In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, emerging, produced, i.e., as we put it, with the potential infinite. But this is not the proper infinite. That we have for instance when we consider the entirety of the numbers 1, 2, 3, 4, ... itself as a completed unit, or the points of a line as an entirety of things which is completely available. That sort of infinity is named actual infinite." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925) p. 167]

> I can see why no one
> else is interested in WMaths,

You are mistaken. It is simply classical mathematics.
>
> Do you, honestly, stand in front of serious minded-students and tell
> them that even though you can't define set (or collection) membership,

Of course I can do it for all practical purposes. See my books. But here we have a much more involved discussion. And I am very glad that you have recognized the key feature:

WM's "first that is deleted" is the key. [...] "which was the first O to be swapped out?" as if this were a reasonable question.

This is really the key! A bijection à la Cantor requires that every pair can be found, when looking for it. But we know that |ℕ|*(|ℕ|-1) O's remain in the matrix over all steps that can be found. The indices of these fractions cannot be found. The belief in Cantor's claims requires to believe that all O's will leave the matrix in individually verifiable terms of the sequence but that this is not individually verfiable for any term.

Regards, WM


zelos...@gmail.com

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Nov 30, 2022, 7:24:10 AM11/30/22
to
Classical mathematics works with modern mathematics, you don't work because YOU'RE AN IDIOT!

Ben Bacarisse

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Nov 30, 2022, 8:17:47 PM11/30/22
to
WM <askas...@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

> Ben Bacarisse schrieb am Mittwoch, 30. November 2022 um 03:32:13 UTC+1:
>> WM <askas...@gmail.com> writes:
>>
>> > Ben Bacarisse schrieb am Montag, 28. November 2022 um 22:33:23 UTC+1:
>>
>> >> One Great
>> >> Theorem of WMaths: the existence of sets X and Y with Y ∈ X and, here
>> >> comes the surprise, X \ {Y} = X.
>> >
>> > In potential infinity the sets, or better collections, are not static.
>> So A \ A might sometimes be {} and sometimes not.
>
> In potential infinity infinite collections change.

Non-responsive. You don't like addressing any detailed points, do you?

>> I can see why no one
>> else is interested in WMaths,
>
> You are mistaken. It is simply classical mathematics.

Classical mathematics can define set membership, equality and
difference. And in classical mathematics if X ∈ Y then X \ {Y} is not
equal to X.

>> Do you, honestly, stand in front of serious minded-students and tell
>> them that even though you can't define set (or collection) membership,
>
> Of course I can do it for all practical purposes.

Do you tell them you can't do it for all purposes such as proving the
Great Theorem of WMaths?

--
Ben.

WM

unread,
Dec 1, 2022, 7:29:30 AM12/1/22
to
Ben Bacarisse schrieb am Donnerstag, 1. Dezember 2022 um 02:17:47 UTC+1:
> WM <askas...@gmail.com> writes:

> > You are mistaken. It is simply classical mathematics.
> Classical mathematics can define set membership, equality and
> difference. And in classical mathematics if X ∈ Y then X \ {Y} is not
> equal to X.

Can you find an X-O matrix with less than |ℕ|*(|ℕ|-1) O's?
Do all these matrices have |ℕ|*(|ℕ|-1) O's in your opinion?

Regards, WM

zelos...@gmail.com

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Dec 1, 2022, 7:39:15 AM12/1/22
to
your X and O argument is irrelevant to cardinal arithmetic you retard

JVR

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Dec 1, 2022, 10:14:19 AM12/1/22
to
Are you really unable to comprehend the fact that "less than" is
meaningless in this context?
Galileo knew this. Perhaps the Greeks already knew it. Every
beginning math student knows it.

WM

unread,
Dec 1, 2022, 11:45:43 AM12/1/22
to
JVR schrieb am Donnerstag, 1. Dezember 2022 um 16:14:19 UTC+1:
> On Thursday, December 1, 2022 at 1:29:30 PM UTC+1, WM wrote:
> > Ben Bacarisse schrieb am Donnerstag, 1. Dezember 2022 um 02:17:47 UTC+1:
> > > WM <askas...@gmail.com> writes:
> >
> > > > You are mistaken. It is simply classical mathematics.
> > > Classical mathematics can define set membership, equality and
> > > difference. And in classical mathematics if X ∈ Y then X \ {Y} is not
> > > equal to X.
> > Can you find an X-O matrix with less than |ℕ|*(|ℕ|-1) O's?
> > Do all these matrices have |ℕ|*(|ℕ|-1) O's in your opinion?
> >
> Are you really unable to comprehend the fact that "less than" is
> meaningless in this context?

I know that it is meaningful, in particular if all elements of the set ℕ are existing and "not a single one of this epitome has been forgotten". And I am very glad that your clumsy utterings are the only counter argument.

> Galileo knew this. Perhaps the Greeks already knew it.

They did not believe in actual or completed infinity. But they already knew that less than |ℕ| is 50, and less than 50 is 0.

> Every
> beginning math student knows it.

Unfortunately most are flooded with the matheologial nonsense which their teachers have never recognized as such.

Regards, WM

WM

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Dec 1, 2022, 11:49:49 AM12/1/22
to
zelos...@gmail.com schrieb am Donnerstag, 1. Dezember 2022 um 13:39:15 UTC+1:
> torsdag 1 december 2022 kl. 13:29:30 UTC+1 skrev WM:

> > Can you find an X-O matrix with less than |ℕ|*(|ℕ|-1) O's?
> > Do all these matrices have |ℕ|*(|ℕ|-1) O's in your opinion?

> your X and O argument is irrelevant to cardinal arithmetic

Cardinal arithmetic is irrelevant to everything relevant.

Regards, WM

Gus Gassmann

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Dec 1, 2022, 12:21:22 PM12/1/22
to
On Thursday, 1 December 2022 at 12:45:43 UTC-4, WM wrote:
> JVR schrieb am Donnerstag, 1. Dezember 2022 um 16:14:19 UTC+1:
> > On Thursday, December 1, 2022 at 1:29:30 PM UTC+1, WM wrote:
> > > Ben Bacarisse schrieb am Donnerstag, 1. Dezember 2022 um 02:17:47 UTC+1:
> > > > WM <askas...@gmail.com> writes:
> > >
> > > > > You are mistaken. It is simply classical mathematics.
> > > > Classical mathematics can define set membership, equality and
> > > > difference. And in classical mathematics if X ∈ Y then X \ {Y} is not
> > > > equal to X.
> > > Can you find an X-O matrix with less than |ℕ|*(|ℕ|-1) O's?

Since you never actually defined what you mean by X-O matrices, I can find buckets of them:

XXX...
XXX...
XXX...
...

OXX...
XXX...
XXX...
...

I could go on...

> > > Do all these matrices have |ℕ|*(|ℕ|-1) O's in your opinion?

Every one of those that I intended to write down has a finite number of 'O's.

In particular, note the first matrix. It contains 0 'O's. That is less than |ℕ|, just in case you hadn't noticed.

Gus Gassmann

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Dec 1, 2022, 12:22:24 PM12/1/22
to
On Thursday, 1 December 2022 at 12:49:49 UTC-4, WM wrote:
> zelos...@gmail.com schrieb am Donnerstag, 1. Dezember 2022 um 13:39:15 UTC+1:
> > torsdag 1 december 2022 kl. 13:29:30 UTC+1 skrev WM:
>
> > > Can you find an X-O matrix with less than |ℕ|*(|ℕ|-1) O's?
> > > Do all these matrices have |ℕ|*(|ℕ|-1) O's in your opinion?
> > your X and O argument is irrelevant to cardinal arithmetic
> [Everything coming from WM] is irrelevant to everything relevant.

Sergi o

unread,
Dec 1, 2022, 12:45:15 PM12/1/22
to
just had to repeat the well known truth;

WM's arithmetic is irrelevant to everything relevant.



WM, sometimes you just have to admit you are wrong, instead of continuing further down that path.
Already you cannot defend any of your "math".
You can spray it onto your students held hostage in class, but they dump it all after the course is over.

it is clear, all underpinnings of Math have been cut away from you.

WM

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Dec 1, 2022, 1:29:37 PM12/1/22
to
Gus Gassmann schrieb am Donnerstag, 1. Dezember 2022 um 18:21:22 UTC+1:
> On Thursday, 1 December 2022 at 12:45:43 UTC-4, WM wrote:

> > > > Do all these matrices have |ℕ|*(|ℕ|-1) O's in your opinion?

OXX...
XXX...
XXX...
...

> Every one of those that I intended to write down has a finite number of 'O's.
>
> In particular, note the first matrix. It contains 0 'O's. That is less than |ℕ|, just in case you hadn't noticed.

If you did it my way, then it contains |ℕ|*(|ℕ|-1) + 1 O's,

Regards, WM

Gus Gassmann

unread,
Dec 1, 2022, 3:34:05 PM12/1/22
to
On Thursday, 1 December 2022 at 14:29:37 UTC-4, WM wrote:
[...]
> If you did it my way, then it contains |ℕ|*(|ℕ|-1) + 1 O's,

XXX...
XXX...
XXX...
...

is still associated with your process as the limit matrix. It has 0 'O's, which last time I looked, was less than |ℕ|*(|ℕ|-1) + 1 (which, of course, has always been simply |ℕ|. Since your way and in particular the descri[tion of what you intended to do is screwed up beyond repair, you had better not ask anyone to follow your bullshit.

Ben Bacarisse

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Dec 1, 2022, 8:17:22 PM12/1/22
to
WM <askas...@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

You are such an intellectual coward! At least stand up for your
nonsense! You explain X ∈ Y and X \ {Y} = X with the fact that in
potential infinity, sets (or collections) change! I say that renders it
useless and your patently silly reply to that was

>> > You are mistaken. It is simply classical mathematics.

When presented with clear evidence from your own posts that "potential
infinity" is clearly not just classical mathematics:

>> Classical mathematics can define set membership, equality and
>> difference. And in classical mathematics if X ∈ Y then X \ {Y} is not
>> equal to X.

Your reply is to simply switch to talking about something else! Defend
it! Explain it! Do sets change over time or is the weather? Can they
change back after lunch? Or maybe they change just with the power of
thought? Can I think an element into your N and will it then be in my N
the as well? Why don't you subscript your sets because N_tuesday may
not be equal to N_wednesday? No wonder you have to distract attention
from WMaths!

WMaths, in which sets change, X ∈ Y but X \ {Y} = X is possible, and set
equality, membership and difference can't be defined so as to explain
such silliness is *not* "simply classical mathematics".

--
Ben.

zelos...@gmail.com

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Dec 2, 2022, 1:01:14 AM12/2/22