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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 8 Dec 2024 09:48:16 +0100
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Am 08.12.2024 um 02:33 schrieb Chris M. Thomasson:
> On 12/7/2024 1:38 PM, Moebius wrote:
>> Am 07.12.2024 um 22:20 schrieb Chris M. Thomasson:
>>
>>> Have you ever implemented a Cantor Pairing function that can go back 
>>> and forth wrt the original number to unique pair and back to the 
>>> original number? They are pretty fun to play around with.
>>
>> Actually, I've implemented a complete library for (finite) "sets" in 
>> C. :-)
>>
> 
> Well, that's fine. Wrt this subject its all about a Cantor pairing. Take 
> any natural, (yes zero works as well) and be able to map it into a 100% 
> unique pairing. Then say okay, we have this unique pair. Now, we are 
> able to take said unique pair and map it right back to the natural that 
> created it to begin with.

Indeed!

https://en.wikipedia.org/wiki/Pairing_function#Inverting_the_Cantor_pairing_function
and
https://en.wikipedia.org/wiki/Pairing_function