Re: Does the number of nines increase?

Am 09.07.2024 um 18:53 schrieb WM:

Either there is a first unit fraction or this is not the case.

It is not the case.
Hint: If s is a unit fraction, 1/(1/s + 1) is a smaller one.

If it is not the case, then NUF(x) increases by more than 1, say by X, at that x where it is leaving 0.

1. NUF does not "increase" but "jump".
2. "That x where it is leaving 0" does not exist. :-)
Hint: NUF(x) = 0 for all x e IR, x <= 0 and NUF(x) = aleph_0 for all x e IR, x > 0.

But then there must exist an x <bla bla bla>

Hint: For all x e IR, x > 0 there are infinitely many unit fractions which are smaller than x. Namely the unit fractions 1/(ceil(1/x + 1), 1/(ceil(1/x + 2), 1/(ceil(1/x + 3), ...
Wie dumm kann man eigentlich sein, Mückenheim?