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.
 Regards, WM