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

On 02.01.2025 19:19, Jim Burns wrote:

On 1/2/2025 6:31 AM, WM wrote:

On 31.12.2024 21:26, Jim Burns wrote:

On 12/31/2024 1:20 PM, WM wrote:

 

Every union of FISONs which
stay below a certain threshold
stays below that threshold.
Note: Every FISON stays below 1 % of ℕ.

>
For each finite ⟦0,j⦆, there are
more.than.#⟦0,j⦆.many finite ⟦0,k⦆

>
So it is for all definable natural numbers.

 So it is for each finite.ordinal.

That is impossible, because all finite ordinals can be subtracted from ℕ without infinitely many remaining. If you don't understand that, it is useless to go on.

natural numbers which have only few successors
because when they are removed nothing remains
ℕ \ {1, 2, 3, ...} = { } .

 ... the non.finite.ordinal natural.numbers.
 We define natural.numbers to be
only finite.ordinals, of which
there are more.than.any.finite.many.

Infinitely many can be removed without remainder. But only finitely many can be defined by FISONs.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
ℕ \ {1, 2, 3, ...} = { }
Di you understand that?

If you want to know how Bob disappears,

I know that he never disappears because he is swapped only inside the matrix.
Regards, WM