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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: Tue, 12 Nov 2024 15:30:25 +0100
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On 12.11.2024 12:23, joes wrote:
> Am Tue, 12 Nov 2024 09:58:12 +0100 schrieb WM:

>> Therefore I prove it. The set of intervals I(n) = [n - 1/10, n + 1/10]
>> cannot cover all fractions on the real axis.
> It absolutely does, for all fractions n.

The claim however is for all fractions q, most of which are different 
from n.

The density is provably 1/5 for all finite initial segments of the real 
line. The sequence 1/5, 1/5, 1/5, ... has the limit 1/5. By translating 
intervals neither their size nor their multitude changes. Therefore 
never more than 1/5 of the real axis is covered. Most rationals remain 
naked.

Regards, WM