Re: Incompleteness of Cantor's enumeration of the rational numbers

Am Wed, 20 Nov 2024 13:04:04 +0100 schrieb WM:

On 19.11.2024 17:42, FromTheRafters wrote:

WM submitted this idea :

 

 > There is a bijection.
Only between numbers which have more successors than predecessors,
although it is claimed that no successors are remaining.

You are not making any sense.

It is not claimed.

Try to count to a natural number that has fewer successors than
predecessors. Impossible.

Because there are no such numbers.

But set theory claims that all natural numbers
can be counted to such that no successors remain.

Fuck no. Get your quantifiers in order: every single natural number
is very clearly finite; the cardinal number corresponding
to the set of all of them is countably infinite.

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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.