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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Fri, 6 Sep 2024 22:01:16 -0400
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On 9/6/24 8:22 AM, WM wrote:
> On 06.09.2024 00:36, Python wrote:
>> Le 05/09/2024 à 22:44, crank Wolfgang Mückenheim, aka WM a écrit :
> 
>>>
>>> You are mistaken. I do not conclude the latter from the former. I 
>>> conclude the latter from the fact that NUF(0) = 0 and NUF(x>0) > 0 
>>> and never, at no x, NUF can increase by more than 1.
>>
>> What the Hell could mean "to increase at an x" ?
> 
> Example: The function f(x) = [x] increases at every x ∈ ℕ by 1.
> The function NUF(x) increases at every x = unit fraction 1/n by 1.
> It does not increase at 0 because 0 is not a unit fraction.
> 
> Regards, WM

Except that is can't because there is no "smallest" unit fraction to 
count from.

Thus, either NUF(x) increases at some sub-finite values, or it doesn't 
exists.

Sorry, you just don't understand that you need to show existance and not 
just presume it.