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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 22 Nov 2024 12:05:58 +0100
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On 22.11.2024 09:52, Mikko wrote:
> On 2024-11-21 19:22:39 +0000, WM said:

>>> True but irrelevant because it may be even closer to the end of
>>> another interval.
>>
>> Every end of any interval is irrational.
> 
> Irrelevant to the claim that a point outside of all intervals has two
> nearest intervals

What else should it have?

> and also to the claim that there is a point outside
> of all intervals

That is proven by the measure of the intervals being less than 3.

> and also to the topic specified on the subjec line.

That is concerned by the fact that in the complement of measure oo - 3 
rational numbers must exist.

> All those claims are true for some sets of intervals and false for others.

Let me know what else than an irrational number could be next to a point 
in the complement, if there were no rational numbers.

Regards, WM