Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 12/7/2024 1:06 AM, Moebius wrote:

Am 06.12.2024 um 20:46 schrieb Chris M. Thomasson:

On 12/5/2024 11:06 PM, Moebius wrote:

Am 06.12.2024 um 01:30 schrieb Chris M. Thomasson:

On 12/5/2024 8:08 AM, WM wrote:

On 05.12.2024 13:26, Richard Damon wrote:
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Which ones can not be "taken" or "given".

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Those with less than infinitely many successors.

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Mückenheim, bei Dir sind wirklich ein paar Schrauben locker.
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Indeed! Numbers which do not exist can not be "taken" or "given" Mückenheim is completely right here! On the other hand, "those"?!
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Do you even know how to take any natural number, create a unique pair and then get back to the original number from said pair?

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I certainly don't know. Please tell me!

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Take any natural number and run it through Cantor Pairing to get a unique pair. From this pair alone we can also get back to the original number.

 Where can I find those natural numbers? And what EXACTLY do you mean by "run it through Cantor Pairing"? I and how does it _create_ pairs?
 Strange things are going on.

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.
https://en.wikipedia.org/wiki/Pairing_function