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

On 10.01.2025 21:03, joes wrote:

Am Fri, 10 Jan 2025 20:22:44 +0100 schrieb WM:

If actual infinity is invariable, then we can take the set ℕ and
consider it as invariable. When we add further elements, it grows.

The set N u {w}, for example, is not equal to N. You can't call
that invariable.

Every set in ZF is invariable.

 

Afterwards it contains further elements. Same can be accomplished by
multiplying all natural numbers by 2.

There is no natural n such that 2*n is not natural.

That it true for every definable number and proves potential infinity.
It contradicts actual infinity. If ***all*** natural numbers are doubled, then you get more than you started with or you did not start with ***all*** natural numbers.
Regards, WM