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

Am 17.07.2024 um 17:27 schrieb WM:

Le 17/07/2024 à 17:21, Moebius a écrit :

Am 17.07.2024 um 17:08 schrieb WM:
>

There is a point where NUF is 0

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Yes, for all points x <= 0.
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and then it increases.

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No, it does not "increase", it _jumps_ "at" x = 0.

 Jumping by [aleph_0] at a point x requires [aleph_0] unit fractions at that point x.

It seems that you have forgotten your OWN definition of NUF, Mückenheim.
No, it does not "require aleph_0 unit fractions at that point x" but aleph_0 unit fractions THAT ARE <= x. (Holy shit!)
Hint: NFU(x) := |{u e {1/n : n e IN} : u <= x}|
Hence:

        NUF(x) = 0 for all x e IR, x <= 0
and
        NUF(x) = aleph_0 for all x e IR, x > 0

<Nonsense deleted>