Re: how

Le 13/06/2024 à 14:22, Jim Burns a écrit :

On 6/12/2024 4:33 PM, WM wrote:

>
there is no j ∈ ℕ after ℕ

>
i.e., after all natural numbers.

 there is no
natural number after (≥) all natural numbers.

But there are many after all definable natural numbers.

I have placed proposal 2 (sets: E A X) and
proposal 3 (meta.sets: E A X C MX) before you.
They have different consequences.

We have the facts above. Your proposals don't change them and don't explain them.

 If each finite von Neumann ordinal
is deleted from
the set of finite von Neumann ordinals,
nothing is left in the result.

That proves that not each one has successors. Otherwise the successors would remain undeleted.

 We finite beings cannot perform a supertask,
which is what it takes to count all
finite von Neumann ordinals.

But if all could be deleted without remainder and if all were definable, then you finite being JB could define one ordinal with no successors.

 However,
it is not a supertask

That would not be a supertask either.
Regards, WM