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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: Tue, 10 Sep 2024 12:05:23 -0700
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On 9/10/2024 11:42 AM, Chris M. Thomasson wrote:
> On 9/10/2024 4:09 AM, FromTheRafters wrote:
>> Chris M. Thomasson brought next idea :
>>> On 9/9/2024 11:49 AM, WM wrote:
>>>> On 09.09.2024 17:27, Python wrote:
>>>>> Le 09/09/2024 à 17:15, Prof. Dr. Mückenheim, aka WM a écrit :
>>>>>> On 09.09.2024 16:32, Python wrote:
>>>>>>> Le 09/09/2024 à 12:19, Prof. Dr. Mückenheim, aka WM a écrit :
>>>>
>>>>> 1/n is not in (0, x). Sure. So what? Nevertheless there are Aleph_0 
>>>>> unit
>>>>> fractions in (0, x). No need for 1/n to be there, there far enough 
>>>>> other
>>>>> fractions.
>>>>>
>>>> If you cannot understand mathematics consider the simplest logic:
>>>> If a sequence of different real points exists on the positive real 
>>>> axis, then it has a beginning. Otherwise it could be a cloud but not 
>>>> a sequence.
>>>
>>> Oh wow. You need help! Or we do for even giving you the time of day. 
>>> YIKES!!!!!!!!!!
>>
>> Actually, I think he is close to correct. The thing is, he wants the 
>> first term of the sequence to be last. The reals are not a sequence, 
>> but the unit fractions are and they start with 1/1 not at some 
>> imagined other end. You need a first and likely a next to start.
> 
> So, I am thinking there is a unit fraction that fits in the simple gap 
> of 1/1 and 1/2:
> 
> 1/1----->1/4------>1/2
> 
> ?
> 
> Fair enough? Is this getting on track or going off the rails?

Actually, there are infinite unit fractions in that gap wrt going off 
the rails wrt _strict_ unit fraction ordering...