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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 23 Sep 2024 01:44:19 +0200
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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).