Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 16.10.2024 17:34, Jim Burns wrote:

On 10/16/2024 4:50 AM, WM wrote:

 

There is a general rule not open to further discussion:
When doubling natural numbers we obtain natural numbers which have
not been doubled.

CORRECTION:
When doubling natural numbers we obtain even numbers which have not
been doubled.

The set S of ordinals which are finite  and for which their double is
not finite is empty.

Maybe. Then not all natural numbers have been doubled.

When doubling natural numbers (finite ordinals)
we obtain natural numbers.

Maybe.

When doubling all natural numbers we obtain only natural numbers.

That is impossible.

In potential infinity we obtain more even natural numbers than have
been doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.

There is a general rule not open to further discussion:
The natural numbers ℕ equal the finite ordinals 𝕆ᶠⁱⁿ

That is only possible in potential infinity. But there the result is
worthless.