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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 6 Nov 2024 11:01:21 +0100
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On 06.11.2024 03:48, Ross Finlayson wrote:
> On 11/05/2024 02:29 AM, Mikko wrote:

>>> Geometry is only another language for the same thing.
>>
>> Another language is an unnecessary complication that only reeasls
>> an intent to deceive.

It is a clearer language.
>>
>> No, the meaning is clear. Of course, because some intevals overlap,
>> you should have specified what exacly you mean by "nearer". But as
>> ε shriks the overlappings disappear and the distance between any
>> two intevals approaches the distance between their centers we may
>> define distance between the intervals as the distance between their
>> endpoints even wne ε > 0.

I leave ε = 1. No shrinking. Every point outside of the intervals is 
nearer to an endpoint than to the contents.

Regards, WM