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

On 17.01.2025 01:37, Richard Damon wrote:

On 1/16/25 8:18 AM, WM wrote:

On 15.01.2025 20:54, joes wrote:

Am Wed, 15 Jan 2025 18:58:40 +0100 schrieb WM:

On 14.01.2025 13:37, Richard Damon wrote:
>

EVERY Natural Number is "Definable",

Then remove the set ℕ by application of only definable numbers:
ℕ \ {1} \ {1, 2} \ {1, 2, 3} \ ...

Yes, N \ {1, 2, 3, ...} = {}.

>
Of course. But what FISON can be dropped?
>

Of course no FINITE (the F of FISON) will be the match for the INFINITE
set of Natural Numbers.
 
That doesn't mean the whole set of them fail, but of course, you need
to be using logic that CAN use *ALL* of them

 
Logic says that every FISON which is smaller than another FISON can be
dropped. Logic says even more: Every FISON which is smaller than ℕ can
be dropped. Therefore all can be dropped.
Do you know a FISON that is smaller than ℕ but cannot be dropped?