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

Am 17.07.2024 um 17:08 schrieb WM:

There is a point where NUF is 0

Yes, for all points x <= 0.

and then it increases.

No, it does not "increase", it _jumps_ "at" x = 0.
MEANING:
        NUF(x) = 0 for all x e IR, x <= 0
and
        NUF(x) = aleph_0 for all x e IR, x > 0
Not that hard, is it?

How?

Huh?! Ask it, it might tell you!
A reasonable question might be: "Why?"
Because for each and every x e IR, x > 0 there are countably-infinitely many unit fractions which are <= x (hint: No first one) AND for each and every x e IR, x <= 0 there is no unit fractions which is <= x.
Not that hard, is it?