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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: Mon, 18 Nov 2024 11:58:07 +0200
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On 2024-11-17 12:46:29 +0000, WM said:

> On 17.11.2024 13:28, Mikko wrote:
>> On 2024-11-17 10:29:31 +0000, WM said:
>> 
>>> Your J'(n) = (n/100 - 1/10, n/100 + 1/10) are 100 times more than mine.
>>> For every reordering of a finite subset of my intervals J(n) the 
>>> relative covering remains constant, namely 1/5.
>>> The analytical limit proves that the constant sequence 1/5, 1/5, 1/5, 
>>> ... has limit 1/5. This is the relative covering of the infinite set 
>>> and of every reordering.
>> 
>> My J'(n) are your J(n) translated much as your translated J(n) except
>> that they are not re-ordered.
>> 
>> My J'(n) are as numerous as your J(n): there is one of each for every
>> natural number n.
> 
> There are 100 intervals for each natural number.
> This can be proven by bijecting J'(100n) and J(n). My intervals are 
> then exhausted, yours are not.

Irrelevant.

>> Each my J'(n) has the same size as your corresponding J(n): 1/5.
> 
>> One more similarity is that neither is relevant to the subject.
> 
> Only if you believe in matheology and resist mathematics.

In mathematics unproven claims do not count.

> Geometry says that your intervals cover the real line, my do not.

Geometry is mathematics so unproven claims do not count.

-- 
Mikko