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