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

On 10/15/2024 08:51 AM, 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"?
>

That doubling _all_ natural numbers only yields _all_ natural numbers is
impossible.

Of course. But all doubled naturals are themselves natural.
>

Aliquot parts, i.e. density where the "half of the integers are even",
and the equivalency of the countably infinite, where "integers are
1-1 squares" were around centuries and THOUSANDS of years before
Grosseteste and Galileo, and are such OLD HAT that this "old wrapped
as new" is long, long, long past its freshness dating.