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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: Wed, 25 Sep 2024 13:22:30 -0400
Organization: i2pn2 (i2pn.org)
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On 9/25/24 11:14 AM, WM wrote:
> On 24.09.2024 23:47, FromTheRafters wrote:
>> on 9/24/2024, WM supposed :
> 
>>> The function NUF(0) increases. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 proves that 
>>> it can gain only one unit fraction at any point x ∈ ℝ, hence NUF has 
>>> to pass the value 1.
>>
>> It means "For all" and says nothing about starting somewhere, moving, 
>> and ending somewhere else.
> 
> Whatever it means. I see that there are no unit fractions below 0 and 
> many above 0. Therefore NUF increases. At no point it can increase by 
> more than 1.

Why not? The problem is that points are "dense" so you can't find a 
"first" point to start at.

At no point can it increase by one, as to go from a finite value to one 
higher, it needs to only have a finite number of unit fractions below 
it, but there is no first unit fraction to start the count, and at any 
finite value, since it has already gotten to Aleph_0, that can't be 
incrmented by one.

So, your NUF just is built on false concepts.

> 
> Even if most mathematicians are far too stupid to understand this, I 
> will repeat it on and on, maybe that sometime some will get it.

No, YOU are just too stupid because you think in terms of finite sets.

> 
> Regards, WM
>