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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 22 Nov 2024 10:52:16 +0200
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On 2024-11-21 19:22:39 +0000, WM said:

> On 21.11.2024 12:01, Mikko wrote:
>> On 2024-11-21 10:50:32 +0000, WM said:
>> 
>>> On 21.11.2024 10:21, Mikko wrote:
>>>> On 2024-11-04 10:47:39 +0000, WM said:
>>> 
>>>>>>> That is wrong. The measure outside of the intervals is infinite. Hence 
>>>>>>> there exists a point outside. This point has two nearest intervals
>>>>>> 
>>>>>> No, it hasn't.
>>>>> 
>>>>> In geometry it has.
>>>> 
>>>> Depends on the set of intervals.
>>> 
>>> No. Every point in the complement is closer to the end of an interval 
>>> than to its contents of rationals.
>> 
>> 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 and also to the claim that there is a point outside
of all intervals and also to the topic specified on the subjec line.
All those claims are true for some sets of intervals and false for others.

-- 
Mikko