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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 22 Nov 2024 11:53:32 +0100
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On 22.11.2024 09:42, Mikko wrote:
> On 2024-11-21 11:03:28 +0000, WM said:

>> For every finite (0, n] the relative covering remains f(n) = 1/10, 
>> independent of shifting. The constant sequence has limit 1/10.
> 
> That is irrelevant to your question whether the whole interval becomes
> black if the shifted intervals (n/2, n/2+1) are painted black.

It is relevant by three reasons:
1) The limit of the sequence f(n) of relative coverings in (0, n] is 
1/10, not 1. Therefore the relative covering 1 would contradict analysis.
2) Since for all intervals (0, n] the relative covering is 1/10, the 
additional blackies must be taken from the nowhere.
3) Since a shifted blacky leaves a white unit interval where it has 
left, the white must remain such that the whole real axis can never 
become black.

These facts prevent the Cantor-bijection for different sets of natural 
numbers.
> 
> And that question is irrelevant to the topic specified on the subject line.
> 
If different sets of natural numbers already cannot be in bijection, 
then the rationals are also excluded.

Regards, WM