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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: Mon, 9 Sep 2024 18:26:32 +0200
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Am 09.09.2024 um 17:27 schrieb Python:
> Le 09/09/2024 à 17:15, Crank Mückenheim, aka WM a écrit :
>> On 09.09.2024 16:32, Python wrote:
>>> Le 09/09/2024 à 12:19, Crank Mückenheim, aka WM a écrit :
>>
>>>> ℵo unit fractions cannot fit into one of the ℵo intervals between 
>>>> two of them.
>>>
>>> (O, x) is NOT an interval between two unit fractions.
>>
>> 1/n - 1/(n+1) = x is an interval between two unit fraction. [WM}
> 
> No. It is a number.

Right. Actually, it's a unit fraction! :-)

| x = 1/k - 1/(k+1) = 1/[k*(k+1)] > 0

Hence x =  1/[k*(k+1)] e {1/n : n e IN}.

>> This interval is shifted to the origin, yielding the interval (0, x). 
>> It does not contain ℵo unit fractions. It does not contain 1/n.
> 
> 1/n is not in (0, x). Sure. So what? Nevertheless there are Aleph_0 unit
> fractions in (0, x). No need for 1/n to be there, there far enough other
> fractions.

Right, for example the infinitely many unit fractions 1/(1/x + 1), 
1/(1/x + 2), 1/(1/x + 3), ...

:-P

What a crank. "Teaching" at a "Hochschule". <facepalm>