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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: =?UTF-8?Q?Re=3A_There_is_a_first/smallest_integer_=28in_M=C3=BCcken?=
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Date: Wed, 17 Jul 2024 18:02:17 +0200
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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 
>>
>> Yes, for all points x <= 0.
>>
>>> and then it increases.
>>
>> No, it does not "increase", it _jumps_ "at" x = 0.

MEANING:

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

> [NFU(x) = 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}|

<Nonsense deleted>