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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: Mon, 18 Nov 2024 23:16:22 +0100
Organization: A noiseless patient Spider
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On 18.11.2024 22:58, FromTheRafters wrote:
> on 11/18/2024, WM supposed :
>> On 18.11.2024 18:15, FromTheRafters wrote:
>>> WM brought next idea :
>>
>>>>> |ℕ| - |ℕ| = 0 because if you subtract one element from ℕ then you have
>>>> no longer ℕ and therefore no longer |ℕ| describing it.
>>>
>>> Still wrong.
>>
>> If you remove one element from ℕ, then you have still ℵo but no longer 
>> all elements of ℕ.
> 
> But you do have now a proper subset of the naturals the same size as 
> before.

It has one element less, hence the "size" ℵo is a very unsharp measure.
> 
>> If |ℕ| describes the number of elements, then it has changed to |ℕ| - 1.
> 
> Minus one is not defined.

Subtracting an element is defined. |ℕ| - 1 is defined as the number of 
elements minus 1.
> 
>> If you don't like |ℕ| then call this number the number of natural 
>> numbers.
> 
> Why would I do that when it is the *SIZE* of the smallest infinite set.

The set of prime numbers is smaller.

Regards, WM