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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: Mon, 25 Nov 2024 14:41:22 +0200
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On 2024-11-24 14:19:06 +0000, WM said:

> On 24.11.2024 13:56, Mikko wrote:
>> On 2024-11-22 11:05:58 +0000, WM said:
>> 
>>> 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?
>> 
>> For every point that is neither an endpoint nor interior point of any
>> of the intervals there is no nearest interval because between that point
>> and any interval there is another interval.
> 
> Wrong. Starting from that point a cursor, by simplest logic, will 
> either touch nothing or something. If it touches something, it can only 
> be an irrational endpoint.

Your "wrong" is wrong. It will either touch something or nothing. If it
touches nothing it cannot touch an irrational endpoint.

-- 
Mikko