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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: Mon, 9 Sep 2024 16:32:11 +0200
Organization: CCCP
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Le 09/09/2024 à 12:19, Crank Mückenheim, aka WM a écrit :
> On 08.09.2024 22:34, Python wrote:
>> 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
> 
> Nonsense. 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. It has, anyway,
the same length that another interval that is between two neighboring
unit fractions.

Ask one your students^H^H^H^H^H^H^H^H^H victims. They know better
than you.