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

Am 17.07.2024 um 16:43 schrieb WM:

Le 17/07/2024 à 13:37, Moebius a écrit :

WM> All unit fractions are separated. Therefore there is a first one
>
Moebius> All integers are separated. Therefore there is a first one [?]
>
WM> This is true but difficult to understand.

 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.)
Not that hard, is it?
Relevance concerning your nonsensical claim "This is true but difficult to understand"? - None.