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

Am 14.10.2024 um 18:15 schrieb Moebius:

Am 14.10.2024 um 18:04 schrieb joes:

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 [of ordinal numbers which lie] "before" ω.

>

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, ..., ω, ω+2, ω+4, ..., ω*2

>
Just let Mückenhirn know:
>
     An e IN: n*2 < ω .
>
Proof: An e IN: n*2 e IN (easy) and An e IN: n < ω. qed

 Hint@Mückenhirn:
      0 < 1 < 2 < 3 < 4 < 5 < 6 < ... < ω ,
 "hence":
      0 < 2 < 4 < 6 < ... < ω .