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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: Thu, 21 Nov 2024 12:03:28 +0100
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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.

Regards, WM
>