Re: More complex numbers than reals?

WM <wolfgang.mueckenheim@tha.de> writes:

Le 15/07/2024 à 00:39, Ben Bacarisse a écrit :

WM <wolfgang.mueckenheim@tha.de> writes:

>

You can define equinumerosity any way you like.

>
And I can prove that Cantor's way leads astray.

But no journal will touch it.  I can't remember which crank excuse you
use to explain that.

>
Simple: The journals are owned by matheologians and stupids. I have never
tried to address them.

*ticks crank excuse bingo card*

Further all that stuff including this proof has been published as a book.
>

Presumably that's why you teach history courses now -- you can avoid
having to write down even the most basic definitions of WMaths sets.

>
At the end of the course I talk about the present state of the art.

Do you cite the journal that has published your proof that Cantor is
wrong?

>
I could do so:
>
"Does Set Theory Cause Perceptual Problems?", viXra 2017-02-26 "Not
enumerating all positive rational numbers", viXra 2017-02-26  "The union is
not the limit.", viXra 2017-03-06  "Failure of the Diagonal Argument",
viXra 2017-03-13 "Set Theory or Slipper Animalcule: Who Wins?", viXra
2017-03-13 "Proof of the existence of dark numbers (bilingual version)",
viXra (Nov 2022)
"Shortest Proof of Dark Numbers", viXra (May 2023)
"Seven Internal Contradictions of Set Theory", viXra (Dec 2023)
"Transfinity - A Source Book", SSRN-Elsevier (April 2024)
"Proof of the existence of dark numbers (bilingual version)", OSFPREPRINTS
(Nov 2022)
"Dark natural numbers in set theory", ResearchGate, October 2019
"Dark natural numbers in set theory" II, ResearchGate, October 2019
"Transfinity - A Source Book", ResearchGate, October 2019 "What scatters
the space?", MResearchGate, May 2020 "Countability Contradicted",
ResearchGate, February 2022
"Proof of the existence of dark numbers (bilingual version)", ResearchGate,
Nov 2022
"The seven deadly sins of set theory", ResearchGate, Dec 2023
"Dark numbers", Academia.edu (2020) "Transfinity - A Source Book",
Academia.edu (31 Dec 2020) "Countability contradicted", Academia.edu (Feb
2022) "Proof of the existence of dark numbers (bilingual version)",
Academia.edu (Nov 2022)
"The seven deadly sins of set theory", Academia.edu (Dec 2023)
"Dark numbers", Quora (May 2023)
"Sequences and Limits", Advances in Pure Mathematics 5, 2015, pp. 59 - 61.
"Transfinity - A Source Book", ELIVA Press, Chisinau 2024.

So no peer reviewed publications.  We knew that, of course.

But I do not quote all that (some of the above with over 1000 reads - more
than usual for maths journals) like I do not quote Newton's or Euler's or
Gauss' or Cauchy's original essays.
>

Do you give the "proper" definitions for set membership,

>
That cannot be done for potentially infinite collections because they have
no fixed membership.

Ah, OK.  So there is no way to prove any theorems about WMaths sets
because there are no definitions of even the most basic terms.

difference and equality once you admit that those in your textbook are
only approximations?  Do you present a proof of the "surprising" result
that sets E and P exist with E in P and P \ {E} = P?

So how did you know that for the E and P we talked about six years ago
that E in P and P \ {E} = P?  Was it all just how you felt at the time?
Is it still true today, or have the sets changed in the last six years
and it's no longer true?  I have to ask because in WMaths set membership
difference and equality can't be defined, so all anyone can do to find
out what you laughingly call "proper mathematics" says is to ask you.
You (apparently) "know" (or knew) that E in P even though you can't
prove it.

--
Ben.