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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? (infinitary)
Date: Thu, 31 Oct 2024 19:43:20 -0400
Organization: i2pn2 (i2pn.org)
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On 10/31/24 1:33 PM, WM wrote:
> On 31.10.2024 12:36, Richard Damon wrote:
>> On 10/31/24 5:31 AM, WM wrote:
> 
>> The problem is functions don't "grow" at a point
> 
> Step functions like NUF do.

No, they change at a value.

> 
>> NUF(x) has an infinite slope at x = 0, as the unit fractions have an 
>> accumulaton point there.
> 
> Wrong. In spite of the accumulation point, all unit fractions exist at 
> different points separated by uncountably many points. The accumulation 
> point has only been invented when the facts were not clear. By the way 
> the accumulation point shows that dark numbers exist. Infinitely many 
> unit fractions cannot be distinguished.
> 
> Regards, WM
> 

Right, but there is no first point, so no point for NUF(x) to make a 
step to 1 at, only to infinity.

Why do you think that all those points can't be distinguished.

They all have a finite value, and thus all are distinguished.

Your logic just can't handle them.