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From: Python <python@invalid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 7 Sep 2024 16:05:24 +0200
Organization: CCCP
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Le 07/09/2024 à 15:03, WM a écrit :
> 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). 

Of course they can.

"There's Plenty of Room at the Bottom" — Richard Feynman.

> The distance between two unit fractions already is larger.

Some are, but for ℵo pairs of them they be arbitrary small
(i.e. < x).

How can you be so wrong on such elementary stuff Crank Mückenheim?