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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: Wed, 27 Nov 2024 11:12:46 +0100
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On 26.11.2024 18:50, Richard Damon wrote:
> On 11/26/24 11:59 AM, WM wrote:
>> 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.
> 
> But maybe you can't and get something consistant.

Of course. |{1, 2, 3, 4, ...}| = |ℕ| and |{2, 3, 4, ...}| = |ℕ| - 1 is 
consistent.

Regards, WM