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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: Thu, 21 Nov 2024 12:59:04 +0200
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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).

-- 
Mikko