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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Mon, 11 Nov 2024 21:33:28 +0100
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On 11.11.2024 19:23, Jim Burns wrote:
> On 11/11/2024 3:41 AM, WM wrote:

>>>> But it will never complete
>>>> an infinite set of claims.
>>>
>>> We do not need an infinite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀 completed.
>>> We do not want an infinite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀 completed.
>>
>> But you claim that
>> _all_ fractions are in bijection with
>> all natural numbers,
>> don't you?
> 
> Yes, I claim that.

For that claim you need an infinite set of claims.

> This is one 𝗰𝗹𝗮𝗶𝗺:
> ⎛ All fractions are in bijection with
> ⎝ all natural numbers.

It is wrong.

>> My intervals I(n) = [n - 1/10, n + 1/10]
>> must be translated to all the midpoints
>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5,
>> 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1, ...
>> if you want to contradict my claim.
> 
> Your 𝗰𝗹𝗮𝗶𝗺𝘀 start with "Sets change".

No, I claim that intervals can be translated. (The set of intervals 
remains constant in size and multitude.) For every finite subset this is 
possible.

Regards, WM