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

On 1/14/25 3:34 AM, WM wrote:

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.

And nothing more needs to fit inbetween, as double evey Natural Number is an already existing Natural Number, so none were created.

 

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

 Nonsense.

Yes, YOU are 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.

Nope, that is your stupidity talking, doubling infinity keeps it at infinity.

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

 True for all definable natnumbers. Wrong for natnumbers > ω/2.

There are no Natural Numbers > omega / 2 as Omega / 2 is just omega.
You are just showing that you don't know what infinity actually is.

 Regards, WM