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Date: Mon, 08 Jul 24 20:11:45 +0000
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From: WM <wolfgang.mueckenheim@tha.de>
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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.
>>>
>>> (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