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

On 15.10.2024 17:51, joes wrote:

Am Mon, 14 Oct 2024 18:37:31 +0200 schrieb WM:

On 14.10.2024 18:04, joes wrote:

Am Mon, 14 Oct 2024 15:40:01 +0200 schrieb WM:

On 14.10.2024 14:15, joes wrote:
>

No, we are taking the complete, actually infinite set which reaches
to "before" w.

and fills the space between 0 and ω evenly. Same happens with the
doubled set between 0 and ω2.

No, there is no consequent infinity. The even numbers do not go 0, 2,
4, ..., w, w+2, w+4, ..., w*2

Either the doubled numbers are natural, then half of them have not been
among the original set, or all natural numbers have been doubled, then
the result contains infinite numbers.

Which "half"?

There is a genaral rule not ope to further discussion:
When doubling natural numbers we obtain natural numbers which have not been doubled.
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.
Regards, WM