Re: How many different unit fractions are lessorequal than all unit fractions?

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).