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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: Thu, 21 Nov 2024 20:22:39 +0100
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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.

> In particular with Cantor's set of intervals
> where there is no nearest interval.

For every point of the complement, every interval has irrational ends.

Regards, WM