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From: Python <python@invalid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sun, 8 Sep 2024 22:34:01 +0200
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Le 08/09/2024 à 21:28, Crank Mückenheim, aka WM a écrit :
> On 07.09.2024 16:05, Python wrote:
>> Le 07/09/2024 à 15:03, WM a écrit :
> 
>>> Stop that nonsense. ℵo unit fractions cannot fit into every interval 
>>> (0, x). 
>>
>> Of course they can.
> 
> Select any gap between one of the first ℵo unit fractions and its 
> neighbour. Call its size x. 

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

> Then ℵo unit fractions cannot fit into the 
> interval (0, x), independent of the actual size.

It can and it does : { 1/p : p > k*(k+1) } has cardinal ℵo,
contains only unit fractions, and is a subset of (0, x)

Ask one of your "students" if you don't understand, crank.