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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 15:59:54 -0500
Organization: Peripheral Visions
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WM used his keyboard to write :
> On 17.11.2024 20:08, joes wrote:
>> Am Sun, 17 Nov 2024 18:38:00 +0100 schrieb WM:
>
>>> Of course. ℵo equals |ℕ|, equals |ℚ|, equals all countable sets. It is
>>> simply another name for infinitely "many". |ℕ| however is a fixed
>>> infinite number. Note that sets are invariable.
>> 
>> Yes, those are all the same number.
>> 
> It is the "number" many. ℚ has all elements of ℕ and some more. Therefore the 
> correct numbers are different.

It is sometimes better to think of cardinality as a number indicating a 
notion of 'set size' rather than a notion of 'number many'. For finite 
sets these two notions merge.