Re: There is a first/smallest integer (in Mückenland)

Le 17/07/2024 à 19:01, joes a écrit :

Am Wed, 17 Jul 2024 15:08:30 +0000 schrieb WM:

Le 17/07/2024 à 16:56, Moebius a écrit :

Am 17.07.2024 um 16:43 schrieb WM:

 

Can you explain how NUF(x) can [jump] from 0 [at x = 0] to [aleph_0]
[at any]
point x [> 0] although all unit fractions are separated by finite
distances [...]

 Yes, of course: For each and every x e IR, x > 0 there are
countably-infinitely many unit fractions which are <= x. (Hint: No
first one.)

 Thema verfehlt. The question is: How does NUF(x) increase from 0 to
more? There is a point where NUF is 0 and then it increases. How?

The same as the sign function.

No, ℵo finite intervals do not fit between [0, 1] and (0, 1]. The sign function fits.

There simply is no such "point", as
there is no least positive number. The distances between unit
fractions get infinitely small.

They remain finite in every case.
Regards, WM