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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Fri, 4 Oct 2024 11:53:50 +0200
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On 04.10.2024 10:29, joes wrote:
> Am Thu, 03 Oct 2024 20:25:07 +0200 schrieb WM:
>> On 02.10.2024 22:07, Jim Burns wrote:
>>> On 10/2/2024 7:12 AM, WM wrote:
>>>> On 01.10.2024 22:05, Jim Burns wrote:
>>>
>>>>> For every nonzero distance d from 0 there are ℵ₀.many unit.fractions
>>>>> closer than d
>>>> That means there is no d by what you can distinguish ℵ₀ unit
>>>> fractions?
>>> You (WM) require us to guess what you mean by 'distinguish'.
>> You distinguish two unit fractions 1/n and 1/m if you place a point in
>> distance d from 0 between them: 1/n < d < 1/m.
> Which is always possible.

For a finite collection of unit fractions. For almost all unit fractions 
it is impossible.
> 
>>> There is no d between ℵ₀.many.smaller.unit.fractions and
>>> slightly.fewer.than.ℵ₀.many.smaller.unit.fractions.
>> That means you cannot distinguish ℵ₀ smaller unit fractions.
> Misconception: there is no „slightly fewer than ℵ₀”.

Of course there is fewer, namely zero. If slightly fewer is not 
possible, then ℵ₀ unit fractions sit at one point.

Regards, WM