Re: Does the number of nines increase?

Le 09/07/2024 à 19:07, Moebius a écrit :

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.

Then there are more first unit fractions.

 Hint: If s is a unit fraction, 1/(1/s + 1) is a smaller one.

This is in contradiction with mathematics: Only one unit fraction at one point.

 

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".

But not by more than 1 at any x.

 2. "That x where it is leaving 0" does not exist. :-)

Wrong worship of matheology.
In mathematics NUF(x) is leaving x not without a unit fraction.

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

Wrong worship of matheology.

 

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.

Not for x between these unit fractions.
Regards, WM