Re: how

Le 18/06/2024 à 19:12, Jim Burns a écrit :

If all numbers having ℵ₀ followers are removed
then no numbers remain.

Note that the ℵ₀ followers are not removed.

There is no first number remaining.

Correct.

There is no number remaining.

Wrong.

 We can _define_ a number that remains;

No.

however,
the _existence_ of the number defined
leads to self.contradiction

Therefor you cannot define a number that remains. But we know the remainder from the fact, that you never have removed ℵo numbers individually.
Definable numbers have finite initial segments. Never more than a finite set is possible.
Regards, WM