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

Am Fri, 06 Dec 2024 10:01:43 +0100 schrieb WM:

On 06.12.2024 00:48, Richard Damon wrote:

On 12/5/24 11:08 AM, WM wrote:

On 05.12.2024 13:26, Richard Damon wrote:
>

Which ones can not be "taken" or "given".

Those with less than infinitely many successors. Cantor claims that
all numbers are in his bijections. No successors remaining.

Which since such numbers don't exist,

If so, then infinity cannot be used completely.

Just because you can't picture infinity?

"The infinite sequence thus defined has the peculiar property to contain
the positive rational numbers completely, and each of them only once at
a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
None is missing, let alone a natural number or infinitely many
successors.

And each of them has infinitely many successors, for which the same goes,
and which are all included (together with their successors, which form
a subset).

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.