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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Tue, 26 Nov 2024 17:59:40 +0100
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On 26.11.2024 16:06, Richard Damon wrote:
> On 11/26/24 6:24 AM, WM wrote:
>> On 26.11.2024 12:15, FromTheRafters wrote:
>>> WM pretended :
>>
>>>> It is impossible to change |ℕ| by 1 or more.
>>>
>>> Right, sets don't change. The set {2,3,4,...} does not equal the set 
>>> of natural numbers, but |{2,3,4,...}| does equal |N|.
>>>
>> Then your |N| is an imprecise measure. My |N| is precise.
>> |{2,3,4,...}| = |N| - 1 =/= |N| .

> Then your measure is incorrect, as by the DEFINITION of measures of 
> infinite sets, all countably infinite sets have the same "measure".

That is one special definition of a very imprecise measure. We can do 
better.

Regards, WM