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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 17 Nov 2024 11:59:17 -0500
Organization: Peripheral Visions
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WM pretended :
> On 17.11.2024 12:38, FromTheRafters wrote:
>> WM presented the following explanation :
>>> On 17.11.2024 12:01, FromTheRafters wrote:
>>>> WM was thinking very hard :
>>>>> On 16.11.2024 22:33, Moebius wrote:
>>>>>
>>>>>> For example "aleph_0 - aleph_0" is not defined.
>>>>>
>>>>> Small wonder. ℵo means only infinitely many: |ℕ|, |ℚ|, and many others.
>>>>> |ℕ|-|ℕ| however is defined.
>>>>
>>>> No, it is not.
>>>
>>> If sets are invariable then ℕ \ ℕ is empty.
>>> If |ℕ| concerns only the elements of ℕ, then |ℕ|-|ℕ|= 0.
>> 
>> So, you're saying that if I take aleph_zero natural numbers and I remove 
>> the aleph_zero odd numbers from consideration in a new set, I will have a 
>> new emptyset instead of E?
>
> Try to understand. "aleph_0 - aleph_0" is not defined.

Try to understand that |N| equals aleph_zero.