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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 22 Nov 2024 12:37:12 -0800
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On 11/22/2024 6:51 AM, WM wrote:
> On 22.11.2024 13:32, joes wrote:
>  > Am Fri, 22 Nov 2024 13:00:52 +0100 schrieb WM:
> 
>  >>>>>>>> The number of ℕ \ {1} is 1 less than ℕ.
>  >>>>>>> And what, pray tell, is Aleph_0 - 1 ?
>  >>>>>> It is "infinitely many" like Aleph_0.
>  >>> Thanks for agreeing with |N| = |N\{0}|.
>  >> Of course. ℵo means nothing but infinitely many.
>  > Good. Then we can consider those sets to have the same number.
>  >
> That is the big mistake. It makes you think that the sets of naturals 
> and of prime numbers could cover each other.

prime numbers are a sub set of the naturals. They are both infinite.