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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Wed, 6 Nov 2024 17:04:44 +0200
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On 2024-11-06 10:01:21 +0000, WM said:

> 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, what can be said about numbers can be stated at least as clearly
in the language of arithmetic.

>>> 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.

This discussion started with message that clearly discussed limits when
ε approaches 0. The case ε = 1 was only about a specific unimportant
question.

-- 
Mikko