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From: Moebius <invalid@example.invalid>
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Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sun, 8 Sep 2024 02:17:45 +0200
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Am 07.09.2024 um 23:51 schrieb Chris M. Thomasson:

>> The unit fractions are identical because they sit at the same x, but 
>> they differ because they are ℵo different unit fractions.

Mückenheim, für jedes x e IR, x > 0, sind die "ℵo different unit 
fractions" 1/ceil(1/x + 1), 1/ceil(1/x + 2), 1/ceil(1/x + 3), ... 
allesamt KLEINER als x. Außerdem sind sie paarweise verschieden. Heißt: 
An,m e IN: n =/= m -> 1/ceil(1/x + n) =/= 1/ceil(1/x + m). Also, nein, 
they DON'T "sit at the same x".

Man kann das auch so hinschreiben: Für jedes x e IR, x > 0:

       0 < ... < 1/ceil(1/x + 3) < 1/ceil(1/x + 2) < 1/ceil(1/x + 1) < x.

Dein Gelaber wird zunehmend wirrer, Mückenheim.

____________________________________________________________________

Man kann da auch gleich den "Beweis" für den Umstand einflechten, dass 
es keinen kleinsten Stammbruch gibt:

       0 < ... < 1/(1/s + 1) < s < ... < 1/ceil(1/x + 3) < 1/ceil(1/x + 
2) < 1/ceil(1/x + 1) < x.