Re: The reality of sets, on a scale of 1 to 10

On 04/03/2025 06:49 AM, WM wrote:

On 02.04.2025 21:39, joes wrote:

There are never empty rooms, all rooms are
always occupied,

>
Are there new guests?
>

that's kinda the point. And yet it can accommodate
a countable number of guests, unlike if it were finite.

>
You confuse the cardinal number and the reality. More rooms or more
guests have same cardinal number. But that is irrelevant because the
cardinal number says nothing. It is a pity however that many, many
thousands of young students have been stultified to helieve what you
wrote above. That is not counterintuitive but it is simply bullshit.
>
Regards, WM
>

Set theory is merely a theory of only one relation
that happens to be only transitive.
All the rest is description and model theory.
The counting and numbering are at least two different things.
What results is a greater consideration of a heno-theory,
what's theory of relation, a model theory.
Then, Zermelo-Fraenkel set theory merely axiomatizes
a few restrictions of comprehension then otherwise
explores a rather simplified theory of sets.
The geometry and number theory then for the
arithmetizations, algebraizations, geometrizations,
have for an overall account of mathematics.
"A Theory"