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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 7 Sep 2024 15:06:08 +0200
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On 07.09.2024 04:01, Richard Damon wrote:
 > On 9/6/24 8:07 AM, WM wrote:

 >> NUF(x) must grow. It cannot grow by more than 1 at any x.
 >> Right or wrong in your opinion?

 > Only if it exists.

There is no reason to deny its existence. If there is zero and all real 
numbers x > 0 and if there are unit fractions, then we can ask how many 
unit fractions are between 0 and any x.
 >
 > If it does, it must be counting some sub-finite values as "unit 
fractions" that are not the reciprocal of the Natural Numbers

Only reciprocals of natural numbers are counted.

 > (since there is no smallest of those unit fractions to count from).

Perhaps you consider only definable natural numbers. They have no 
largest element.

 > Maybe that is your dark numbers, these sub-finite numbers that are 
reciprocals of some post-finite values above the infinite set of Natural 
Numbers (which have no upper bound) and are below Omega.

Dark numbers are post finitely definable.

Regards, WM