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

On 10/27/24 12:12 PM, WM wrote:

Am 27.10.2024 um 14:54 schrieb Moebius:

Am 27.10.2024 um 08:38 schrieb WM:
>

and after NUF(x') = 1

>
There is no x' e IR such that NUF(x') = 1.

 If all unit fractions are existing, then there is each one. Never two or more are at the same point. Hence there is a single one first.

No two together, but no need for one to be first at the large 'n' end of them.
That is the nature of being infinite.

>
Hint: For each and every x e IR, x <= 0: NUF(x) = 0
and for each and every x e IR, x > 0: NUF(x) = aleph_0.

 That is blatantly wrong because it would require that ℵo unit fractions exist between 0 and each and every x > 0, i.e., the open interval (0, 1].
 Regards, WM
 

Right, like is what happens.
It may seem strange to a person stuck in finite logic, but is true when you understand how infinity works.