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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: Sun, 22 Sep 2024 18:33:13 -0700
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On 9/22/2024 4:44 PM, Moebius wrote:
> Am 23.09.2024 um 01:35 schrieb Moebius:
>> Am 23.09.2024 um 01:28 schrieb Chris M. Thomasson:
>>
>> Concerning the integers:
>>
>>> [...} each number has infiniteLY MANY predecessors and infiniteLY 
>>> MANY successors.
>>
>> ...
> 
> Btw. we might define "signed unit fractions" too (just for fun).
> 
> Def.: x e IR is a /signed unit fraction/ iff there is an z in Z such 
> that x = 1/z.
> 
> Then the signed unit fractions are just the numbers
> 
>     -1/1, -1/2, -1/3, ... ... 1/3, 1/2, 1/1.
> 
> 0 would be a very special point here. No signed unit fraction, but 
> "surrounded" by infinitely many signed unit fractions. Moreover, they 
> would be arbitrarilly dense "there" (i.e. in the environment of 0).
> 
> 

Indeed they would. Kind of reminds me a new fractal I made using a 
single line as a starting point. It creates a square out of the line:

https://www.facebook.com/share/p/xHrCG6wRHYp9QrhS