Two similar properties with different results

[WM]

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]

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!
309 views
by zelos...@gmail.com Sep 23, 2022, 12:15:59 AM


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


Re: My fucking of her corpse
309 views
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
88 views
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"
29 views
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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• 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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◦ #487 in Electromagnetic Theory
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◦ #8,751 in Electromagnetism (Books)

[Sergi o]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

a BOT for sure!

[Ben Bacarisse]

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]

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]

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]

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]

Classical mathematics works with modern mathematics, you don't work because YOU'RE AN IDIOT!

[Ben Bacarisse]

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]

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]

your X and O argument is irrelevant to cardinal arithmetic you retard

[JVR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Nope, it is relevant to sets which is relevant to all of mathematics. Your stuff is not

[WM]

Gus Gassmann schrieb am Donnerstag, 1. Dezember 2022 um 21:34:05 UTC+1:
> 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.

Of course.

> It has 0 'O's

That is the question. Are they remaining in the darkness? Or have they left the matrix? When have the O's gone? As much is clear because it is provable: They have not gone in any definable step. That however would be necessary if all fractions could be indexed.

> |ℕ|*(|ℕ|-1) + 1 (which, of course, has always been simply |ℕ|.

No, that would follow from the just disproved mapping. Since there is no bijection between naturals and fractions, there is no equality between |ℕ|*|ℕ| and |ℕ|, not even between |ℕ| and |ℕ| + 1.

Regards, WM

[WM]

Ben Bacarisse schrieb am Freitag, 2. Dezember 2022 um 02:17:22 UTC+1:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)

> You explain X ∈ Y and X \ {Y} = X with the fact that in
> potential infinity, sets (or collections) change!

A simple example is the set of known prime numbers.

Regards, WM

[WM]

zelos...@gmail.com schrieb am Freitag, 2. Dezember 2022 um 07:01:14 UTC+1:
> torsdag 1 december 2022 kl. 17:49:49 UTC+1 skrev WM:

> > Cardinal arithmetic is irrelevant to everything relevant.
> >

> Nope, it is relevant to sets which is relevant to all of mathematics.

Concerning the application of transfinite numbers in other mathematical disciplines, the great expectations originally put on set theory have been fulfilled only in few special cases. [W. Felscher: "Naive Mengen und abstrakte Zahlen III", Bibliographisches Institut, Mannheim (1979) p. 25] . in fact in no case at all. See https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 125ff.

Regards, WM

[Python]

This is utterly silly. At some given time this is a *different* set.

Just as if the daily temperature drops from 20°C to 10°C once, it
doesn't mean that the number 20 turns into 10.

It would be fair to expel you from teaching ever again, and condemn
you to jail for abuse of students for years, Mückenheim. You are
an idiotic and disgusting dishonest imbecile.

[WM]

Python schrieb am Freitag, 2. Dezember 2022 um 11:46:32 UTC+1:
> Crank Wolfgang Mückenheiml,aka WM wrote:
> > Ben Bacarisse schrieb am Freitag, 2. Dezember 2022 um 02:17:22 UTC+1:
> >> WM <askas...@gmail.com> writes:
> >> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> >> Unendlichen" at Hochschule Augsburg.)
> >> You explain X ∈ Y and X \ {Y} = X with the fact that in
> >> potential infinity, sets (or collections) change!
> >
> > A simple example is the set of known prime numbers.

> At some given time this is a *different* set.

Over the time it is a function like every potentially infinite set: "something becoming, emerging, produced, i.e., as we put it, with the potential infinite." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925) p. 167]

>
> Just as if the daily temperature drops from 20°C to 10°C once, it
> doesn't mean that the number 20 turns into 10.

But the daily temparature drops like "a 'potential infinity' in the form of an unending process" [H.B. Enderton: "Elements of set theory", Academic Press, New York (1977) p. 14f]

>
> It would be fair to expel you from teaching ever again,

Stupid assertion of an uneducated yobbo.

Regards, WM

[Gus Gassmann]

On Friday, 2 December 2022 at 06:25:51 UTC-4, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 1. Dezember 2022 um 21:34:05 UTC+1:
> > 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.
> Of course.
>
> > It has 0 'O's
>
> That is the question. Are they remaining in the darkness? Or have they left the matrix? When have the O's gone? As much is clear because it is provable: They have not gone in any definable step. That however would be necessary if all fractions could be indexed.

What a fucking load of crap! As I have said for some time, you have no clue about limits. The limit of the sequence 1/1, 1/2, 1/3, ... is zero. There are no bits of positivity lurking in the darkness, and there are no 'O's in the limit matrix. They do not mysteriously leave, just like the bits of positivity in the sequence of reciprocals do not mysteriously leave when you pass to the limit. The limit of the matrix is computed pointwise. (I hope you know what that is, since this is a discussion you are having with Ben Bacarisse who refers you to your own fucking textbook.) And every element of the matrix (which, by the way, occurs at a finite spot (n,m) that has a finite index in the Cantor mapping) is eventually changed from an 'O' to an 'X', and never changes back. More is not needed!

And now please fuck off.

[WM]

Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 12:33:12 UTC+1:
> there are no 'O's in the limit matrix.

Where have they gone? What are their indices?

> And every element of the matrix (which, by the way, occurs at a finite spot (n,m) that has a finite index in the Cantor mapping) is eventually changed from an 'O' to an 'X', and never changes back. More is not needed!

No, that is not true. What are the indices of O's which never have left in a step where the sequence could be stopped?

Regards, WM

[Gus Gassmann]

On Friday, 2 December 2022 at 08:16:43 UTC-4, WM wrote:
> Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 12:33:12 UTC+1:
> > there are no 'O's in the limit matrix.
> Where have they gone? What are their indices?

They are not in the limit matrix. Try to get it through your thick head that omega does not have a predecessor. Because the limit matrix does not contain any 'O' (I gave you the proof many times, although you clearly are too stupid to grasp this), there is no index for a nonexistent object.

> > And every element of the matrix (which, by the way, occurs at a finite spot (n,m) that has a finite index in the Cantor mapping) is eventually changed from an 'O' to an 'X', and never changes back. More is not needed!
> No, that is not true. What are the indices of O's which never have left in a step where the sequence could be stopped?

At any finite step the indices are whatever they are. You can compute them if you want. You can even enumerate each of the 'O's and determine in which position each is at each step of your asinine stepwise process. There will always be infinitely many steps to follow, which is why the limit is needed. And in the limit matrix there is no 'O', hence no index. How difficult can that be to comprehend?

Do you agree that there is no 'O' in the matrix


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

Perhaps an even easier question would be: Is 0, the limit of the sequence 1/1, 1/2, 1/3, ..., a positive number? If not, where do you think the positive numbers all disappeared to?

[Timothy Golden]

On Friday, November 25, 2022 at 5:10:00 AM UTC-5, 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.

Why the lies of the rational numbers have to be repeated over and over here I have no idea. Suffice it to say that 1/2 and 2/4's are enough to falsify this claim.

>
> 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

[WM]

Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 14:00:27 UTC+1:
> On Friday, 2 December 2022 at 08:16:43 UTC-4, WM wrote:
> > Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 12:33:12 UTC+1:
> > > there are no 'O's in the limit matrix.
> > Where have they gone? What are their indices?
> They are not in the limit matrix.

But their fractions should be indexed. "every number p/q comes at an absolutely fixed position of a simple infinite sequence" [E. Zermelo: "Georg Cantor – Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer, Berlin (1932) p. 126]

> Try to get it through your thick head that omega does not have a predecessor.

But every existing fraction should be indexed.

> Because the limit matrix does not contain any 'O' (I gave you the proof many times, ,

No reason. They are not visible. The question is, when did the O's go?

> there is no index for a nonexistent object.

But the fractions were existing.

Look, I have an easier comprehensible definition of "definable number". A definable natural number is an index n in my proof, up to which no O has left the matrix M_n.

> > What are the indices of O's which never have left in a step where the sequence could be stopped?
> At any finite step the indices are whatever they are. You can compute them if you want.

Of course.

> You can even enumerate each of the 'O's and determine in which position each is at each step of your asinine stepwise process. There will always be infinitely many steps to follow, which is why the limit is needed. And in the limit matrix there is no 'O', hence no index. How difficult can that be to comprehend?

That is easy to comprehend. The question however remains, what happens with those |ℕ|*(|ℕ|-1) fractions which remain without index as long as indices are issued?

>
> Do you agree that there is no 'O' in the matrix

None can be seen. If there is none in the matrix, then they all must have left. I cannot imagine how that could have happened by exchanging with X's inside the matrix, but I know that wherever the O's are, their fractions have never been indexed.

>
>
> XXX...
> XXX...
> XXX...
> ...
>
> Perhaps an even easier question would be: Is 0, the limit of the sequence 1/1, 1/2, 1/3, ..., a positive number? If not, where do you think the positive numbers all disappeared to?

Of course 0 is the limit. See W. Mückenheim: "Mathematik für die ersten Semester", 4th ed., De Gruyter, Berlin (2015). The positive numbers need not disappear in potential infinity because 0 is only approached, never reached. In actual infinity they have disappeared in the darkness between every definable term and the limit.

Regards, WM

[Sergi o]

On 12/2/2022 4:36 AM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 2. Dezember 2022 um 07:01:14 UTC+1:
>> torsdag 1 december 2022 kl. 17:49:49 UTC+1 skrev WM:
>
>>> Cardinal arithmetic is irrelevant to everything relevant.
>>>
>> Nope, it is relevant to sets which is relevant to all of mathematics.
>

It would be fair to expel you from teaching ever again, and condemn
you to jail for abuse of students for years, Mückenheim. You are
an idiotic and disgusting dishonest imbecile.

>

> Regards, WM

[Gus Gassmann]

On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:
> Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 14:00:27 UTC+1:
> > On Friday, 2 December 2022 at 08:16:43 UTC-4, WM wrote:
> > > Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 12:33:12 UTC+1:
> > > > there are no 'O's in the limit matrix.
> > > Where have they gone? What are their indices?
> > They are not in the limit matrix.
> But their fractions should be indexed. "every number p/q comes at an absolutely fixed position of a simple infinite sequence" [E. Zermelo: "Georg Cantor – Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer, Berlin (1932) p. 126]
> > Try to get it through your thick head that omega does not have a predecessor.
> But every existing fraction should be indexed.

And it is, you fucking moron! What do you think it means when an 'X' is put where previously there was an 'O'? The limit matrix consists of 'X's only. What do you think that means? How fucking stupid are you, Perfessor Muckenheim, from this great institution of higher learning, Augsburg University of Implied Sciences?

[Chris M. Thomasson]

_known_ prime numbers... wow! You really are finite in your brain...

"Infinite prime numbers" must give you a damn headache?

[Sergi o]

this site says they list ALL prime numbers; (bet they calculate on the fly)

https://www.math.uchicago.edu/~luis/allprimes.html

270029; 270031; 270037; 270059; 270071; 270073; 270097; 270121; 270131; 270133; 270143; 270157; 270163; 270167; 270191; 270209; 270217; 270223; 270229;
270239; 270241; 270269; 270271; 270287; 270299; 270307; 270311; 270323; 270329; 270337; 270343; 270371; 270379; 270407; 270421; 270437; 270443; 270451;
270461; 270463; 270493; 270509; 270527; 270539; 270547; 270551; 270553; 270563; 270577; 270583; 270587; 270593; 270601; 270619; 270631; 270653; 270659;
270667; 270679; 270689; 270701; 270709; 270719; 270737; 270749; 270761; 270763; 270791; 270797; 270799; 270821; 270833; 270841; 270859; 270899; 270913;
270923; 270931; 270937; 270953; 270961; 270967; 270973;

but you have to press Next page a lot...

and the density of primes seems to stay the same...

this is 270000 to 271000 and it has about 95 primes or about 10% are prime


500009; 500029; 500041; 500057; 500069; 500083; 500107; 500111; 500113; 500119; 500153; 500167; 500173; 500177; 500179; 500197; 500209; 500231; 500233;
500237; 500239; 500249; 500257; 500287; 500299; 500317; 500321; 500333; 500341; 500363; 500369; 500389; 500393; 500413; 500417; 500431; 500443; 500459;
500471; 500473; 500483; 500501; 500509; 500519; 500527; 500567; 500579; 500587; 500603; 500629; 500671; 500677; 500693; 500699; 500713; 500719; 500723;
500729; 500741; 500777; 500791; 500807; 500809; 500831; 500839; 500861; 500873; 500881; 500887; 500891; 500909; 500911; 500921; 500923; 500933; 500947;
500953; 500957; 500977; 501001;

another 1000 and there are 80 or about 8%


SO perhaps about 9% of all numbers are prime in any interval (?)

wiki says different;
https://en.wikipedia.org/wiki/Prime_number_theorem

[Chris M. Thomasson]

On 12/2/2022 1:21 PM, Sergi o wrote:
> On 12/2/2022 2:44 PM, Chris M. Thomasson wrote:
>> On 12/2/2022 2:30 AM, WM wrote:
>>> Ben Bacarisse schrieb am Freitag, 2. Dezember 2022 um 02:17:22 UTC+1:
>>>> WM <askas...@gmail.com> writes:
>>>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>>>> Unendlichen" at Hochschule Augsburg.)
>>>> You explain X ∈ Y and X \ {Y} = X with the fact that in
>>>> potential infinity, sets (or collections) change!
>>>
>>> A simple example is the set of known prime numbers.
>>
>> _known_ prime numbers... wow! You really are finite in your brain...
>>
>> "Infinite prime numbers" must give you a damn headache?
>>
>
> this site says they list ALL prime numbers;  (bet they calculate on the
> fly)

[...]

Think of a natural number being able to be described by primes for a
moment... There are an infinite number of naturals, and if any natural
can be described by primes, then there must be an infinite number of
primes. Sound Kosher?

2 = 2 * 1 // already prime
3 = 3 * 1 // already prime
4 = 2 * 2 // 2 is prime
5 = 5 * 1 // 5 is prime
6 = 2 * 3 // 2 and 3 are prime
7 = 7 * 1 // 7 is prime
8 = 2^3 // 2 is prime
9 = 3^2 // 3 is prime
11 = 11 * 1 // 11 is prime
12 = 2^2 * 3 // 2 and 3 are prime
[...]

?

[Chris M. Thomasson]

oh shit, what happened to 10! Damn dark number.

10 = 2 * 5 // 2 and 5 are prime

No so dark anymore! ;^D

[Ben Bacarisse]

"Chris M. Thomasson" <chris.m.t...@gmail.com> writes:

> Think of a natural number being able to be described by primes for a
> moment... There are an infinite number of naturals, and if any natural
> can be described by primes, then there must be an infinite number of
> primes. Sound Kosher?

No, that's not a sound argument. Even if we firm it up a bit and say
that "described by primes" means "is a product of powers of primes"
there are infinite sets of numbers that can be described by a finite set
of primes. The infinity of the described set does not imply there must
be an infinite describing set.

BTW, don't be fooled by WM's example of a changeable potentially
infinite set. It's a red herring. In his silly

X ∈ Y but Y \ {X} = Y

we know the X is in Y. What we have is a claim that subtracting a known
member makes a set that contains the subtracted member. This is a
common crank tactic -- keep saying ever more crazy stuff to distract
from things you regret saying.

--
Ben.

[Ben Bacarisse]

WM <askas...@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

> Ben Bacarisse schrieb am Freitag, 2. Dezember 2022 um 02:17:22 UTC+1:
>> WM <askas...@gmail.com> writes:

>> You explain X ∈ Y and X \ {Y} = X with the fact that in
>> potential infinity, sets (or collections) change!
>
> A simple example is the set of known prime numbers.

You'd really like people to go down this rabbit hole wouldn't you?
After all, words are your friends where symbols are your enemy, but
neither X not Y in your famous X ∈ Y but X \ {Y} = X is anything like
that. X either briefly looses a member (for no reason you have even
been able to provide), or X gains a member before the equality is
asserted.

My challenge was to defend or explain this nonsense, but you can't. All
you can do is admit that the most basic set operations of WMaths can't
be fully defined whilst stupidly stated that "it is simply classical
mathematics". It isn't.

--
Ben.

[Chris M. Thomasson]

On 12/2/2022 2:44 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>
>> Think of a natural number being able to be described by primes for a
>> moment... There are an infinite number of naturals, and if any natural
>> can be described by primes, then there must be an infinite number of
>> primes. Sound Kosher?
>
> No, that's not a sound argument. Even if we firm it up a bit and say
> that "described by primes" means "is a product of powers of primes"
> there are infinite sets of numbers that can be described by a finite set
> of primes. The infinity of the described set does not imply there must
> be an infinite describing set.

Ahhhh.... Touche. Thanks Ben. Well... Humm, did I get a bit better wrt
the following:

If we can prove that there are infinite prime numbers, then they can be
indexed by the naturals, which are infinite:

i[0] = 2
i[1] = 3
i[2] = 5
i[3] = 7
i[4] = 11
i[5] = 13
...
on and on?

Imvvho, there are an infinite number of primes. Am I making the same
mistake here, but if the sqrt of a prime is an irrational, and there are
infinite irrationals... Well, this is not a sound argument, right?

[Fritz Feldhase]

On Saturday, December 3, 2022 at 1:22:59 AM UTC+1, Ben Bacarisse wrote:
> > >
> > > You explain X ∈ Y and X \ {Y} = X

Should read "X ∈ Y and Y \ {X} = Y", right?

> > A simple example is the set of known prime numbers. [WM]

Holy shit!

> You'd really like people to go down this rabbit hole wouldn't you?
> After all, words are your friends where symbols are your enemy,

Indeed!

> in your famous X ∈ Y but X \ {Y} = X [...]

Should read "X ∈ Y and Y \ {X} = Y", right?

[FromTheRafters]

Chris M. Thomasson has brought this to us :

You describe two different infinities. The countable primes and
naturals, and the uncountable irrationals.

[Chris M. Thomasson]

The uncountable irrationals as a whole, has to contain every irrational
that arises from the sqrt of a prime, right? What am I missing here?

[WM]

Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 18:37:08 UTC+1:
> On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:

> > But every existing fraction should be indexed.
> And it is

Not by a definable index, because every definable index leaves |ℕ|*(|ℕ|-1) O's, i.e., |ℕ|*(|ℕ|-1) fractions not indexed-

> What do you think it means when an 'X' is put where previously there was an 'O'?

It means that an O is put where previously was an X.

> The limit matrix consists of 'X's only.

But in no definable step an O has left the matrix. A lossless exchange with losses would violate logic.

> What do you think that means?

Pay attention: In no definable step an O has left the matrix. If however there were dark parts in the matrix from the beginning, then the O's can have gathered there in the end without violating logic.

Regards, WM

[WM]

Ben Bacarisse schrieb am Samstag, 3. Dezember 2022 um 01:22:59 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, 2. Dezember 2022 um 02:17:22 UTC+1:
> >> WM <askas...@gmail.com> writes:
>
> >> You explain X ∈ Y and X \ {Y} = X with the fact that in
> >> potential infinity, sets (or collections) change!
> >
> > A simple example is the set of known prime numbers.
> You'd really like people to go down this rabbit hole wouldn't you?

I like people who understand this kind of math. I feel sorry for people who claim to understand Cantor but cannot understand what potential means.

> My challenge was to defend or explain this nonsense, but you can't.

You are really too stupid to understand that a prime number discovered in the future does not yet belong to the set of known prime numbers? Or that, after mankind has been reduced to 1000 survivers, like 75000 years ago, many prime numbers known today will be no longer known?

Regards, WM

[Gus Gassmann]

On Saturday, 3 December 2022 at 06:39:05 UTC-4, WM wrote:
> Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 18:37:08 UTC+1:
> > On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:
>
> > > But every existing fraction should be indexed.
> > And it is

[...]

> > What do you think it means when an 'X' is put where previously there was an 'O'?
> It means that an O is put where previously was an X.

Pay attention, stupid! It means that an 'X' is put where previously there was an 'O', and that one more fraction has been indexed. Here you prove that you actually understand my argument and are intentionally throwing up smokescreens because you know you have been cooked. From a psychotic arsehole like yourself one shouldn't expect anything else, I suppose.

> > The limit matrix consists of 'X's only.
> But in no definable step an O has left the matrix.

Yes, at every finite step of your asinine stepwise procedure there are infinitely many more steps that you have ahead of you. You will never finish, unlike Cantor, who gave the full formula that applies to *ALL* infinitely many positive fractions. That marks Cantor as *INFINITELY* many more intelligent than you!

> > What do you think that means?

[blubber]

It means that in the limit every fraction has been indexed. Nothing more, nothing less. That you can neither accept nor understand that, is your problem and that of the great institution of higher learning that hired you, Augsburg University of Implied Sciences.

[Julio Di Egidio]

On Saturday, 3 December 2022 at 14:07:22 UTC+1, Gus Gassmann wrote:
> On Saturday, 3 December 2022 at 06:39:05 UTC-4, WM wrote:
> > Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 18:37:08 UTC+1:
> > > On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:

<snip>

> > > The limit matrix consists of 'X's only.
> > But in no definable step an O has left the matrix.
> Yes, at every finite step of your asinine stepwise procedure there are infinitely many more steps that you have ahead of you. You will never finish, unlike Cantor, who gave the full formula that applies to *ALL* infinitely many positive fractions. That marks Cantor as *INFINITELY* many more intelligent than you!
> > > What do you think that means?
> [blubber]
> It means that in the limit every fraction has been indexed

Except that Cantor doe not use limits, which
is quite the crux of the whole conundrum.

Julio

[WM]

Gus Gassmann schrieb am Samstag, 3. Dezember 2022 um 14:07:22 UTC+1:
> On Saturday, 3 December 2022 at 06:39:05 UTC-4, WM wrote:
> > Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 18:37:08 UTC+1:
> > > On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:
> >
> > > > But every existing fraction should be indexed.
> > > And it is
> [...]
> > > What do you think it means when an 'X' is put where previously there was an 'O'?
> > It means that an O is put where previously was an X.

> It means that an 'X' is put where previously there was an 'O', and that one more fraction has been indexed.

No. It means that an 'X' is put where previously there was an 'O', and that the O is put where previously was the X.

> > > The limit matrix consists of 'X's only.
> > But in no definable step an O has left the matrix.
> Yes, at every finite step of your asinine stepwise procedure there are infinitely many more steps that you have ahead of you.

And none of them decreases the number of O's.

> You will never finish, unlike Cantor, who gave the full formula that applies to *ALL* infinitely many positive fractions.

I use his formula and index every fraction according to his formula.

> That marks Cantor as *INFINITELY* many more intelligent than you!

Maybe, but I merely repeat his intelligent procedure.

> It means that in the limit every fraction has been indexed. Nothing more, nothing less.

Maybe, but all definable indices, i.e. those which apply only a lossless exchange, apply only only a lossless exchange.

Regards, WM

[Fritz Feldhase]

On Saturday, December 3, 2022 at 3:20:06 PM UTC+1, WM wrote:

A keeper: "all definable indices, i.e. those which apply only a lossless exchange, apply only only a lossless exchange." [WM]

[Sergi o]

On 12/3/2022 4:50 AM, WM wrote:
> Ben Bacarisse schrieb am Samstag, 3. Dezember 2022 um 01:22:59 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, 2. Dezember 2022 um 02:17:22 UTC+1:
>>>> WM <askas...@gmail.com> writes:
>>
>>>> You explain X ∈ Y and X \ {Y} = X with the fact that in
>>>> potential infinity, sets (or collections) change!
>>>
>>> A simple example is the set of known prime numbers.
>> You'd really like people to go down this rabbit hole wouldn't you?
>
> I like people who understand this kind of math. I feel sorry for people who claim to understand Cantor but cannot understand what potential means.
>
>> My challenge was to defend or explain this nonsense, but you can't.
>
> You are really too stupid to understand that a prime number discovered in the future does not yet belong to the set of known prime numbers?

the "set of prime numbers" consists of ALL prime numbers. There is no time dependence.

you can instead say the "set of prime numbers known today" instead.

sets do not change.

> Or that, after mankind has been reduced to 1000 survivers, like 75000 years ago, many prime numbers known today will be no longer known?

that does not affect the "set of prime numbers" at all.

you can instead say, "the known set of prime numbers 75000 years ago"

>
> Regards, WM


your thinking is muddled and unclear.

[Sergi o]

On 12/3/2022 8:20 AM, WM wrote:
> Gus Gassmann schrieb am Samstag, 3. Dezember 2022 um 14:07:22 UTC+1:
>> On Saturday, 3 December 2022 at 06:39:05 UTC-4, WM wrote:
>>> Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 18:37:08 UTC+1:
>>>> On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:
>>>
>>>>> But every existing fraction should be indexed.
>>>> And it is
>> [...]
>>>> What do you think it means when an 'X' is put where previously there was an 'O'?
>>> It means that an O is put where previously was an X.
>> It means that an 'X' is put where previously there was an 'O', and that one more fraction has been indexed.
>
> No. It means that an 'X' is put where previously there was an 'O', and that the O is put where previously was the X.

see? I told you not to use stickies and pasties, now you got them all mixed up !


Why not just stick to the natural numbers and the fractions ??

Why do you cover them up with your sick little stickies and pasties of X and Os ?

>
>>>> The limit matrix consists of 'X's only.
>>> But in no definable step an O has left the matrix.
>> Yes, at every finite step of your asinine stepwise procedure there are infinitely many more steps that you have ahead of you.
>
> And none of them decreases the number of O's.

that is not the question here.

>
>> You will never finish, unlike Cantor, who gave the full formula that applies to *ALL* infinitely many positive fractions.
>
> I use his formula and index every fraction according to his formula.

no, you stopped. that is why you have stickies all over you!

>
>> That marks Cantor as *INFINITELY* many more intelligent than you!
>
> Maybe, but I merely repeat his intelligent procedure.

you failed, that is expected.

>
>> It means that in the limit every fraction has been indexed. Nothing more, nothing less.
>
> Maybe, but all definable indices, i.e. those which apply only a lossless exchange, apply only only a lossless exchange.

lossless exchange Ants

lossless Ant exchange

Ant lossless exchange


>
> Retards, WM

[Chris M. Thomasson]

On 12/3/2022 6:20 AM, WM wrote:
> Gus Gassmann schrieb am Samstag, 3. Dezember 2022 um 14:07:22 UTC+1:
>> On Saturday, 3 December 2022 at 06:39:05 UTC-4, WM wrote:
>>> Gus Gassmann schrieb am Freitag, 2. Dezember 2022 um 18:37:08 UTC+1:
>>>> On Friday, 2 December 2022 at 10:38:57 UTC-4, WM wrote:
>>>
>>>>> But every existing fraction should be indexed.
>>>> And it is
>> [...]
>>>> What do you think it means when an 'X' is put where previously there was an 'O'?
>>> It means that an O is put where previously was an X.
>> It means that an 'X' is put where previously there was an 'O', and that one more fraction has been indexed.
>
> No. It means that an 'X' is put where previously there was an 'O', and that the O is put where previously was the X.
>
>>>> The limit matrix consists of 'X's only.
>>> But in no definable step an O has left the matrix.
>> Yes, at every finite step of your asinine stepwise procedure there are infinitely many more steps that you have ahead of you.
>
> And none of them decreases the number of O's.
>
>> You will never finish, unlike Cantor, who gave the full formula that applies to *ALL* infinitely many positive fractions.
>
> I use his formula and index every fraction according to his formula.

[...]

You are missing a lot of pairs. Remember that Cantor Pairing creates
pairs that are _not_ proper fractions. 1/0 comes to mind... ;^)

List out the first 42 Cantor Pairings. Can you do it?

[Chris M. Thomasson]

On 12/3/2022 2:50 AM, WM wrote:
> Ben Bacarisse schrieb am Samstag, 3. Dezember 2022 um 01:22:59 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, 2. Dezember 2022 um 02:17:22 UTC+1:
>>>> WM <askas...@gmail.com> writes:
>>
>>>> You explain X ∈ Y and X \ {Y} = X with the fact that in
>>>> potential infinity, sets (or collections) change!
>>>
>>> A simple example is the set of known prime numbers.
>> You'd really like people to go down this rabbit hole wouldn't you?
>
> I like people who understand this kind of math. I feel sorry for people who claim to understand Cantor but cannot understand what potential means.

[...]

Are you a potential moron, or a full-blown moron?

[Chris M. Thomasson]

A little test for you. What index is the following pairing:

(42, 0) ?

It should be easy because Cantor Pairing is bidirectional.

[Ben Bacarisse]

Fritz Feldhase <franz.fri...@gmail.com> writes:

> On Saturday, December 3, 2022 at 1:22:59 AM UTC+1, Ben Bacarisse wrote:
>> > >
>> > > You explain X ∈ Y and X \ {Y} = X
>
> Should read "X ∈ Y and Y \ {X} = Y", right?

Sorry, yes. I got it right in other posts! I've typed it so often my
fingers got away from my brain.

The specific sets (from all those years ago) where the set of even
numbers, and the power set of N. After endless ducking a diving he
eventually agreed that E ∈ P(N) and when I asked "What is P(N) \ {E}" he
said: "Here comes the surprise: P(N) \ {E} = P(|N) because we cannot fix
E".

That nonsense led to his eventually admitting that he could not define
set membership, equality and difference. I don't think he tells his
students that he can't say what these operations are... It's not in the
course notes, as far as I can see.

--
Ben.

[Ben Bacarisse]

I don't see an argument here at all. Any subset of N can be indexed by
N, though finite subsets don't need more than a finite subset of
indexes.

>>> Imvvho, there are an infinite number of primes. Am I making the same
>>> mistake here, but if the sqrt of a prime is an irrational, and there
>>> are infinite irrationals... Well, this is not a sound argument, 
>>> right?
>>
>> You describe two different infinities. The countable primes and
>> naturals, and the uncountable irrationals.
>
> The uncountable irrationals as a whole, has to contain every
> irrational that arises from the sqrt of a prime, right? What am I
> missing here?

Yes. I am not sure what you are missing. Both R and R\Q (the
irrationals) are uncountable. But there are countable subsets of R\Q
(such as the square roots of the primes).

--
Ben.

[Ben Bacarisse]

"Chris M. Thomasson" <chris.m.t...@gmail.com> writes:

It's not a settled question whether zero is in N or not -- different
authors take different views. However, WM has given one correct formula
for the pairing (no idea where he got it from) so I'm not sure what you
think is missing.

--
Ben.

[Sergi o]

I posted it for a while, showing it is only an indexing change, 2D matrix array to 1D linear array, knowing WM cannot deal with equations.
But later on he picked it up, which suprized me, but he still doesn't now how to use it.

WM is stone cold non-math. WM has only posted a few equations, then reposts the same. There is no knowledge displayed by him that he knows how to read
or use, or modify equations. (so WM is still on the BOT list)

[Chris M. Thomasson]

Does he know how to go from a pair back into an index?

[WM]

Fritz Feldhase schrieb am Samstag, 3. Dezember 2022 um 15:25:21 UTC+1:

> A keeper: "all definable indices, i.e. those which apply only a lossless exchange, apply only only a lossless exchange." [WM]

Nevertheless, not endorsed by matheologians. They claim that all definable indices, i.e. those which apply only lossless exchanges, can lose O's.

Regards, WM

[WM]

Ben Bacarisse schrieb am Sonntag, 4. Dezember 2022 um 02:02:52 UTC+1:
> WM has given one correct formula
> for the pairing (no idea where he got it from)

From Cantor of course. Collected Works p.132.
Only for this simple reason I can claim that my matrices repeat his process minutely.

Regards, WM

[Ben Bacarisse]

Probably not. But does that matter? Such formulas have been posted
here before so he could just look one up if pressed.

--
Ben.

[Sergi o]

show a proper URL,

show the publisher, publish date, the proper name of the paper or book, and the author.


or we will know you are making this up.






>
> Regards, WM

[WM]

Ben Bacarisse schrieb am Sonntag, 4. Dezember 2022 um 18:19:01 UTC+1:
> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:

> > Does he know how to go from a pair back into an index?
> Probably not. But does that matter?

Really? The formula yielding the index k from the pair m and n is the heart of my proof. So you have not understood it in the least, but you dare to criticize it as a would-be expert? Thank you for outing yourself as belonging to the same class as these dead losses.

Regards, WM

[Sergi o]

On 12/4/2022 1:05 PM, WM wrote:
> Ben Bacarisse schrieb am Sonntag, 4. Dezember 2022 um 18:19:01 UTC+1:
>> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>
>>> Does he know how to go from a pair back into an index?
>> Probably not. But does that matter?
>
> Really? The formula yielding the index k from the pair m and n is the heart of my proof. So you have not understood it in the least,

no, they are saying YOU probably do not understand the equation.

why do you twist that fact into an excuse to despise others ? Defensive I see.

Your attack is your admission you are not able to read/understand/derive equations.

> but you dare to criticize it as a would-be expert? Thank you for outing yourself as belonging to the same class as these dead losses.
>
> Regards, WM

another KEEPER !!

"you dare to criticize it as a would-be expert" - WM

[Chris M. Thomasson]

Did you ever code up the inverse of Cantor Pairing?

[Chris M. Thomasson]

What index was used to create the pair (42, 0)?

[Chris M. Thomasson]

How about the pair (123, 456)? What index created that pairing?

[Sergi o]

Wonder if he can derive it ? EZ Cheesy !

[Chris M. Thomasson]

He should be able to do it right of the bat! He talks about Cantor
Pairing all the damn time, right? Another question, what is the index
for the following pair:

(666, 666)

? WM can get this right, right? ;^o

[FromTheRafters]

on 12/4/2022, Chris M. Thomasson supposed :

That pair is not there.

[Jim Burns]

Using other people's work is actually pretty normal
in mathematics. Not worth criticizing, if not worth
praising, either.
(Lying about whose work it is is different.)

If WM has read my posts (an open question),
then he has seen formulas for both directions,
pairs-to-indexes and indexes-to-pairs.

Here they come again:

p/q to k
s = p+q
k = (s-1)(s-2)/2+p

k to p/q
s = ceiling((sqrt(8k+1)+1)/2)
p = k-(s-1)(s-2)/2
q = s-p

The problem with this as a quiz for WM
is that WM has already gone off into his
own little world well before he gets to
what you're testing for here.

I'm told he once knew physics, though.
Somehow. <shrug>

[Ben Bacarisse]

Sergi o <inv...@invalid.com> writes:

> On 12/4/2022 4:31 AM, WM wrote:
>> Ben Bacarisse schrieb am Sonntag, 4. Dezember 2022 um 02:02:52 UTC+1:
>>> WM has given one correct formula
>>> for the pairing (no idea where he got it from)
>> From Cantor of course. Collected Works p.132.
>> Only for this simple reason I can claim that my matrices repeat his
>> process minutely.
>
> show a proper URL,
>
> show the publisher, publish date, the proper name of the paper or
> book, and the author.

Odd that someone with an academic background should be so averse to
giving a proper citation.

But the pairing functions isn't in doubt, surely? The one WM got from
somewhere (curiously not written as a function) is correct:

"k = (m + n - 1)(m + n - 2)/2 + m"

> or we will know you are making this up.

WM admits that Cantor never discusses swaps, so the actual case in point
is just made-up by WM. But again, is it in doubt anymore? WM agreed
that the only sane interpretation of his mysterious "final result" is
the limit of a sequence, and he agrees that the limit is what everyone
else says it is. In order to keep going, he's had to make up some
nonsense. There's no disagreement about the swaps and the matrices
anymore.


--
Ben.

[Chris M. Thomasson]

Yes it is.

[Chris M. Thomasson]

On 12/4/2022 1:12 PM, FromTheRafters wrote:

Oh, were you jesting? Shit. Sorry.

[Ben Bacarisse]

Sergi o <inv...@invalid.com> writes:

> On 12/4/2022 1:05 PM, WM wrote:
>> Ben Bacarisse schrieb am Sonntag, 4. Dezember 2022 um 18:19:01 UTC+1:
>>> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>>
>>>> Does he know how to go from a pair back into an index?
>>> Probably not. But does that matter?
>> Really? The formula yielding the index k from the pair m and n is the
>> heart of my proof. So you have not understood it in the least,
>
> no, they are saying YOU probably do not understand the equation.

WM has a point here because I misread what Chris said. WM gave the
formula for the index, and I thought Chris was asking (as he has
elsewhere) about the /inverse/. Even I don't think he can't put two
numbers into a simple formula! Whether he can invert it is what I was
querying...

--
Ben.

[Ben Bacarisse]

"Chris M. Thomasson" <chris.m.t...@gmail.com> writes:

> He should be able to do it right of the bat! He talks about Cantor
> Pairing all the damn time, right? Another question, what is the index
> for the following pair:
>
> (666, 666)

What is the point of this line of questioning? A few months ago he gave
the formula for the index. Do you really think he can't do that trivial
arithmetic? Even I would not doubt it.

You could ask (as indeed I thought you were asking) if he can /invert/
the formula, but that's another matter.

--
Ben.

[Ben Bacarisse]

"Chris M. Thomasson" <chris.m.t...@gmail.com> writes:

> On 12/4/2022 1:12 PM, FromTheRafters wrote:
>> on 12/4/2022, Chris M. Thomasson supposed :
>>> On 12/4/2022 11:05 AM, WM wrote:
>>>> Ben Bacarisse schrieb am Sonntag, 4. Dezember 2022 um 18:19:01 UTC+1:
>>>>> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>>>>
>>>>>> Does he know how to go from a pair back into an index?
>>>>> Probably not. But does that matter?
>>>>
>>>> Really? The formula yielding the index k from the pair m and n is the heart of my proof. So you have not understood it in the least, but
>>>> you dare to criticize it as a would-be expert? Thank you for outing yourself as belonging to the same class as these dead losses.
>>>
>>> What index was used to create the pair (42, 0)?
>> That pair is not there.
>
> Yes it is.

No it isn't. The pairing function (as given by WM) is defined for
n,m >= 1.

--
Ben.

[Jim Burns]

On 12/4/2022 4:41 PM, Chris M. Thomasson wrote:
> On 12/4/2022 1:12 PM, FromTheRafters wrote:
>> on 12/4/2022, Chris M. Thomasson supposed :

>>> What index was used to create the pair (42, 0)?
>>
>> That pair is not there.
>
> Oh, were you jesting? Shit. Sorry.

The pairs are from 1,2,3,... and 1,2,3,...
and the index is from 1,2,3,...
(42, 0) is not in that sequence.

It wouldn't be hard to make a different sequence
in which (42,0) occurs,
but no, it's not in that one. No joke.

(1,1) (1,2) (2,1) (1,3) (2,2) (3,1) (1,4) ...
... (40,2) (41,1) (1,42) (2,41) ...

[Chris M. Thomasson]

On 12/4/2022 1:51 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>
>> He should be able to do it right of the bat! He talks about Cantor
>> Pairing all the damn time, right? Another question, what is the index
>> for the following pair:
>>
>> (666, 666)
>
> What is the point of this line of questioning?

I just wanted to see if he can answer the question. He can say something
like:

The answer is x, then tell me to go f'off or something.

No problem.

> A few months ago he gave
> the formula for the index. Do you really think he can't do that trivial
> arithmetic? Even I would not doubt it.

Humm...

> You could ask (as indeed I thought you were asking) if he can /invert/
> the formula, but that's another matter.

pair to index

index to pair

[Chris M. Thomasson]

OH, I missed one of his rules. What about 0/1 is that a kosher fraction?

[Chris M. Thomasson]

(42, 0) = 903

...
i[902] = (0, 41)
i[903] = (42, 0)
...

[Chris M. Thomasson]

On 12/4/2022 1:53 PM, Ben Bacarisse wrote:

Does the following list work with WM's rules?

i[4] = 1, 1
i[7] = 2, 1
i[8] = 1, 2
i[11] = 3, 1
i[12] = 2, 2
i[13] = 1, 3
i[16] = 4, 1
i[17] = 3, 2
i[18] = 2, 3
i[19] = 1, 4
i[22] = 5, 1
i[23] = 4, 2
i[24] = 3, 3
i[25] = 2, 4
i[26] = 1, 5
i[29] = 6, 1
i[30] = 5, 2
i[31] = 4, 3
i[32] = 3, 4
i[33] = 2, 5
i[34] = 1, 6
i[37] = 7, 1
i[38] = 6, 2
i[39] = 5, 3
i[40] = 4, 4
i[41] = 3, 5
i[42] = 2, 6
i[43] = 1, 7

[Chris M. Thomasson]

On 12/4/2022 1:55 PM, Jim Burns wrote:

[Chris M. Thomasson]

On 12/4/2022 1:53 PM, Ben Bacarisse wrote:

...
i[900] = 2, 39 ********** WM
i[901] = 1, 40 ********** WM
i[902] = 0, 41
i[903] = 42, 0
i[904] = 41, 1 ********** WM
i[905] = 40, 2 ********** WM
...

The pairs (0, 41) and (42, 0) are right in between pairs that follow WM
rules.

[Chris M. Thomasson]

On 12/2/2022 6:24 AM, Timothy Golden wrote:
> On Friday, November 25, 2022 at 5:10:00 AM UTC-5, 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.
>
> Why the lies of the rational numbers have to be repeated over and over here I have no idea. Suffice it to say that 1/2 and 2/4's are enough to falsify this claim.

I am not sure why some people get mad when we reduce 2/4's into 1/2.
Some actually say 1/2 does not equal 2/4... Damn!


>
>>
>> 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