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

Am Sat, 28 Dec 2024 14:58:50 +0100 schrieb WM:

On 28.12.2024 06:23, Moebius wrote:

On 12/17/24 4:51 PM, WM wrote:

 

all FISONs contain/are all n.

All FISONs contain all *definable* n.

Which, in standard mathematics, is all inf. many of them

Hint: For each and every n e IN there is a FISON such that n is in it.
BUT there's no FISON such that each and every n e IN is in it.

Every FISON contains less than half of all natural numbers.

Almost none, actually, N being infinite and all.

Therefore
the union of all of them contains less than half of all natural numbers.

Worng.
--
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.