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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 20 Jan 2025 13:42:58 +0100
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On 19.01.2025 16:05, joes wrote:
> Am Sun, 19 Jan 2025 11:52:33 +0100 schrieb WM:

>> Cantor claims this also for infinite sets: "The infinite sequence thus
>> defined has the peculiar property to contain the positive rational
>> numbers completely, and each of them only once at a determined place."
>> [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
> That's not what that means. Some infinite sets are countable, even though
> you don't "finish" them. The quote refers to a bijection.

But there is no bijection bijection without completeness: to contain the 
positive rational numbers completely.
> 
>>> There is no step from finite to infinite.
>> Not in the visible domain. But there is no loss in lossless exchange -
>> even in the dark domain. There lies your fault.
> There is only a limit, which does have different properties.

A bijection concerns pairing of all elements, no limit. And in 
particular no loss in explicitly lossless exchange.

Regards, WM