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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 28 Sep 2024 22:28:36 +0200
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Am 28.09.2024 um 22:20 schrieb Moebius:
> Am 28.09.2024 um 06:26 schrieb Chris M. Thomasson:
>> On 9/27/2024 3:13 PM, FromTheRafters wrote:
>>> WM expressed precisely :
>>>> On 25.09.2024 19:22, Richard Damon wrote:
>>>>> On 9/25/24 11:14 AM, WM wrote:
> 
>>>>>> NUF increases
> 
> No, it "jumps at 0".
> 
> MEANING: NUF(0) = 0 and Ax > 0: NUF(x) = aleph_0.
> 
>>>>>> At no point it can increase by more than 1.
>>>>> Why not?
>>>>
>>>> Because there is a finite gap between two [adjacent] unit fractions.
> 
> Using WM's mantra: An e IN: 1/n - 1/(n + 1) > 0.

@Mückenheim: Ax > 0: NUF(x) = aleph_0 besagt GENAU, dass für jedes x e 
IR mit x > 0 _abzählbar unendlich_ viele Stammbrüche in (0, x) enthalten 
sind. Und das ist auch richtig (denn es ist so).

Der Umstand, dass trivialerweise An e IN: 1/n - 1/(n + 1) > 0 gilt, tut 
dem keinen Abbruch; auch wenn Du zu doof und zu blöde bist, um das zu 
verstehen.