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

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:
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Concerning the integers:
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[...} each number has infiniteLY MANY predecessors and infiniteLY MANY successors.

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...

 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