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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: Sat, 11 Jan 2025 11:04:56 +0100
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On 11.01.2025 01:28, Richard Damon wrote:
> On 1/10/25 4:48 PM, WM wrote:
>> On 10.01.2025 21:08, Jim Burns wrote:
>>
>>> Where OUR infinityⁿᵒᵗᐧᵂᴹ "doesn't work",
>>> it's you who's saying it doesn't work,
>>
>> You are inconsistent. You claim that all natural numbers are an 
>> invariable set. But when all elements are doubled then your set grows, 
>> showing it is not invariable. That is nonsense.
>>
> But the set doesn't grow.
> 
> Which element is in the doubled set that wasn't there in the first place?

The number of elements remains constant. All odd numbers of ℕ are 
deleted. That implies that new even numbers are added.

"The infinite sequence thus defined has the peculiar property to contain 
the positive rational numbers completely, and each of them only once at 
a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]

If Cantor has constructed a sequence containing all even numbers of the 
original set ℕ, then the doubled even numbers are missing.

Regards, WM