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

Am Sun, 05 Jan 2025 11:32:23 +0100 schrieb WM:

On 04.01.2025 12:05, joes wrote:

Am Sat, 04 Jan 2025 09:42:11 +0100 schrieb WM:

On 1/3/2025 2:48 PM, WM wrote:

On 03.01.2025 19:46, Jim Burns wrote:

>
All finite.ordinals removed from the set of each and only
finite.ordinals leaves the empty set.

But removing every ordinal that you can define (and all its
predecessors) from ℕ leaves almost all ordinals in ℕ.∀n ∈ ℕ_def: |ℕ \
{1, 2, 3, ..., n}| = ℵo

No. One can „define” infinitely many numbers.

Define all such that none remains - like in ℕ \ {1, 2, 3, ...} = { }.

There, you did it.