Re: More complex numbers than reals?

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But I do not quote all that (some of the above with over 1000 reads - more than usual for maths journals) like I do not quote Newton's or Euler's or Gauss' or Cauchy's original essays.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

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?
 Fortunately for you, your college has no degree program in mathematics
so none of your students know better.  Unfortunately for your students,
you don't know better.

There has not yet been any disprove of my simplest proof (that I told you recently and that you were wise enaugh to let it uncommented). The only daredevil who tried it, Jim Burns, has to assume that by exchangig one of the elements can disappear. No reason to pay attention. And the nonsense you once tried to sell to my former students has been rejected by them flatly.
Regards, WM