Re: Does the number of nines increase?

Le 08/07/2024 à 16:35, Moebius a écrit :

Am 08.07.2024 um 16:12 schrieb WM:

Le 08/07/2024 à 04:52, Moebius a écrit :
 

(4) Es gilt also IN DER MENGENLEHRE für alle x e IR, x > 0: |{m e {1/n : n e IN} : m <= x}| = aleph_0.
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(5) Mit der Definition NUF(x) := |{m e {1/n : n e IN} : m <= x}| folgt also für alle x e IR, x > 0: NUF(x) = aleph_0.

 ℵo unit fractions occupy at least ℵo different points on the positive real axis.

 Nicht nur "at least", sondern "genau"

There is no precision, no "genau" with ℵo.

 

Hence NUF(x) = ℵo cannot be true for x less than ℵo points, that is for a set of ℵo positive x.

 Huh?!

You cannot think so far? What a pity.

 NUF(x) = ℵo ist für alle x e IR, x > 0 wahr.

Not for the first ℵo points and their intervals required that the number of unit fractions can grow to ℵo.

Auch in diesem Fall gilt: NUF(0) = 0 und für alle x e IR, x > 0: NUF(x) = aleph_0.
 Das ist alles ziemlich trivial.

You cannot draw the conclusion: If X unit fractions occupy X points, then there cannot exist more than X unit fractions at the first X points. Ob alle Mathematiker zu blöde sind, um das zu verstehen?
Gruß, WM