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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: Wed, 2 Oct 2024 13:57:54 +0200
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On 02.10.2024 13:17, Richard Damon wrote:
> On 10/1/24 1:39 PM, WM wrote:
>> On 01.10.2024 01:14, Richard Damon wrote:
>>> On 9/30/24 11:15 AM, WM wrote:
>>>> On 30.09.2024 00:29, FromTheRafters wrote:
>>>>> WM explained on 9/29/2024 :
>>>>>> On 28.09.2024 00:08, FromTheRafters wrote:
>>>>>>  > WM presented the following explanation :
>>>>>>
>>>>>>  >> Between two unit fractions there is always a finite gap.
>>>>>>  >
>>>>>>  > How big?
>>>>>>
>>>>>> In terms of set theory: uncountably many points.
>>>>>
>>>>> How wide are these points?
>>>>
>>>> More than nothing.
>>>
>>> But it must be next to nothing,
>>
>> No, between them and nothing there are infinitely many countable sets 
>> and then finite sets of points.
> 
> So your "smallest" wasn't the smallest,

Of course all gaps between unit fractions are made of more than finitely 
many points. I never denied that.

>>> which becomes nothing when we get to the actual infinite set.
>>
>> Not in mathematics.
> 
> Sure it does.

Try to learn the basics and to understand ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

Regards, WMK