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

On 14.01.2025 09:02, Moebius wrote:

Am 13.01.2025 um 21:55 schrieb Chris M. Thomasson:

On 1/13/2025 9:17 AM, WM wrote:

 

doubling of all natural numbers creates numbers larger than ω.

 Idiotic nonsense.

Possibly. But it is a direct consequence of actual = completed infinity. If all natural numbers fill the space between 0 and ω such that nothing more fits in between, then nothing more fits in between.

All of those results are natural numbers. They were already there...

Nonsense.

Indeed. (At least in the context of classical mathematics/set theory.)

Doubling changes the number. If all were there already, then all are changed. ∀n ∈ ℕ: 2n > n.

 Using symols:
           An e IN: n*2 e IN .

True for all definable natnumbers. Wrong for natnumbers > ω/2.
Regards, WM