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NNTP-Posting-Date: Fri, 22 Nov 2024 18:42:45 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Fri, 22 Nov 2024 10:42:48 -0800
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On 11/22/2024 07:11 AM, joes wrote:
> Am Fri, 22 Nov 2024 15:51:11 +0100 schrieb WM:
>> 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.
> As it should. You can give each prime an index.
>

The other way though, in Hilbert's 'Otel there's
necessarily bumping each one down each time any is moved.