Re: More complex numbers than reals?

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

Le 14/07/2024 à 03:30, Ben Bacarisse a écrit :

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

Le 13/07/2024 à 02:12, Ben Bacarisse a écrit :

WM <wolfgang.mueckenheim@tha.de> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen"

>
and "Kleine Geschichte der Mathematik"

Optional, I hope.
 

at Hochschule Augsburg.)

>
Meanwhile Technische Hochschule Augsburg.

A sound name change that reflects the technical college's focus.
 

Le 11/07/2024 à 02:46, Ben Bacarisse a écrit :

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

>

{a, b, c} vs { 3, 4, 5 }
>
Both have the same number of elements,

That will fall down for infinite sets unless, by decree, you state that
your meaning of "more" makes all infinite sets have the same number of
elements.

>
There are some rules for comparing sets which are not subset and superset,
namely symmetry:

Still nothing about defining set membership, equality and difference in
WMaths though.

>
Are my rules appearing too reasonable for a believer in equinumerosity of
prime numbers and algebraic numbers?

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.

 But you can't claim the
"surprising" result of WMaths that E in P and P \ {E} = P

>
That refers to potential infinity and dark elements. Visible elements form
only a potentially infinite collection.

You cut the end of the sentence of course because you want to divert
attention from that fact that you can't define set membership,
difference and equality in WMaths.  The waffle words will not get you
past that fact that without those definitions you have no alternative to
offer.

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?  Do you give the "proper" definitions for set 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.

--
Ben.