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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 21 Sep 2024 17:52:56 -0700
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On 9/10/2024 11:38 AM, Chris M. Thomasson wrote:
> On 9/10/2024 11:35 AM, Chris M. Thomasson wrote:
>> On 9/9/2024 5:32 PM, Moebius wrote:
>>> Am 10.09.2024 um 01:08 schrieb Chris M. Thomasson:
>>>
>>>> Take the gap between:
>>>>
>>>> 1/1 and 1/2. There are infinitely many unit fractions that are small 
>>>> enough to fit within that gap.
>>>
>>> Oh, really?! Could you name (just) o n e? :-)
>>
>> 1/4?
> 
> 1/4 is between 1/1 and 1/2:
> 
> 1/1---->1/4---->1/2
> 
> So, its not _strict_ but it does exist... Fair enough? Or crank shit all 
> the way down? It seems that any non-zero gap can have unit fractions 
> small enough to fit in it...
> 
> 
>>
>>
>>>
>>> I mean ... a unit fraction u such that 1/2 < u < 1/1. :-o
>>
>>
> 

1-->3/4-->1/2-->1/4-->0

This can get more granular wrt:

1-->(1/4 + 1/4 + 1/8*2)-->1/2--->(1/16*2 + 1/8)---->0

;^)