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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Fri, 22 Nov 2024 10:42:09 +0200
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On 2024-11-21 11:03:28 +0000, WM said:

> On 21.11.2024 11:59, Mikko wrote:
>> On 2024-11-21 10:21:40 +0000, WM said:
>> 
>>> On 21.11.2024 10:16, Mikko wrote:
>>>> On 2024-11-20 11:42:15 +0000, WM said:
>>> 
>>>>> The intervals before and after shifting are not different. Only their 
>>>>> positions are.
>>>> 
>>>> The intervals are different. A shifted interval contains a different
>>>> set of numbers.
>>> 
>>> Consider this simplified argument. Let every unit interval after a 
>>> natural number n which is divisible by 10 be coloured black: (10n, 
>>> 10n+1]. All others are white. Is it possible to shift the black 
>>> intervals so that the whole real axis becomes black?
>> 
>> Yes. Shift the interval (10n, 10n+1) to (n/2, n/2+1).
> 
> 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.

And that question is irrelevant to the topic specified on the subject line.

-- 
Mikko