Re: More complex numbers than reals?

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.  But you can't claim the
"surprising" result of WMaths that E in P and P \ {E} = P whilst
admitting that you have no workable definition of set membership,
difference or equality.

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

--
Ben.