Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 17.01.2025 15:52, Richard Damon wrote:

On 1/17/25 5:50 AM, WM wrote:

On 17.01.2025 01:37, Richard Damon wrote:

On 1/16/25 10:19 AM, WM wrote:

On 16.01.2025 13:27, Richard Damon wrote:
>

The potential infinity itself isn't growing, our KNOWLEDGE of it
grows as we generate its members.

But the knowledge of actually infinite sets isn't growing?

Depends how good you can think.

No, it has nothing to do with your missing knowledge or your lack of
thinking capability. "Potential infinity refers to a procedure that
gets closer and closer to, but never quite reaches, an infinite end.
[...] Completed infinity, or actual infinity, is an infinity that one
actually reaches; the process is already done."[E. Schechter:
"Potential versus completed infinity: Its history and controversy" (5
Dec 2009)]

That "definition" violates to definition that set don't change.

So it is. But if infinity is potential, then we cannot change this in
order to keep set theory, but then set theory is wrong.
>

Some may talk of a growing set, but then you can't use any logic based
on "fixed" sets.

Correct. If infinity is potential. set theory is wrong.