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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 14 Jan 2025 09:34:36 +0100
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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