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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: Tue, 5 Nov 2024 12:26:58 +0100
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On 05.11.2024 11:29, Mikko wrote:
> On 2024-11-04 18:12:55 +0000, WM said:

>>> There is no nearesst one. There is always a nearer one.

And always the endpoint is irrational.

> That you don't even try to support your clam to support your claim
> indicates that you don't really believe it.

My claim says that every point outside of intervals has an irrational 
interval end next to it. It does not matter how many intervals you claim 
between the point and the nearest interval, because _all_ intervals have 
irrational endpoints.

  Cantor's results are
> conclusions of proofs and you have not shown any error in the proofs.

I have. This example for instance proves that he did not enumerate all 
rationals, because the rationals are dense, the intervals are not dense.

> You are free to deny one of more of the assumptions that constitue
> the foudations of the results but you havn't.

Cantor's bijections concern only potentially infinite sets, but are 
assumed and claimed to concern the complete sets. That is the grave 
mistake. His result says for all infinite "countable sets" that they are 
infinite, nothing more. Mathematics proves that for all intervals (0, 
2n) the ratio between even numbers and natural numbers is 1/2. The 
sequence 1/2, 1/2, 1/2, ... has limit 1/2. That is the true result in 
mathematics.

Regards, WM