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

On 04.01.2025 17:21, joes wrote:

Am Sat, 04 Jan 2025 09:17:16 +0100 schrieb WM:

On 03.01.2025 21:29, joes wrote:

Am Fri, 03 Jan 2025 20:48:57 +0100 schrieb WM:

>

But removing every ordinal that you can define (and all its
predecessors) from ℕ leaves almost all ordinals in ℕ.

No, N is exactly the set of those numbers.

∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo contradicts your opinion.

Where is the contradiction?

You say that every natural number has ℵo successors. That is wrong because ℕ \ {1, 2, 3, ...} = { }. Only every definable number has ℵo successors.
Regards, WM