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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 15:03:35 +0200
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On 07.09.2024 14:37, Richard Damon wrote:
> On 9/7/24 8:04 AM, WM wrote:

>> NUF(x) changes by 1 because a change by more at any x would count more 
>> different unit fractions 1/n,  1/m, 1/k, ... which are identical 
>> because they are the same x = 1/n = 1/m = 1/k = ... .
>>
> And thus is always has a value of aleph_0 for all x > 0, since there is 
> always aleph_0 unit fractions below and finite positive x value.

Stop that nonsense. ℵo unit fractions cannot fit into every interval (0, 
x). The distance between two unit fractions already is larger. And if 
you claim that ℵo unit fractions exist, then you must accept that their 
distances do exist too.

By the way this is independent of the existence of NUF.

Regards, WM