Re: How many different unit fractions are lessorequal than all unit fractions?

WM was thinking very hard :

On 07.09.2024 21:01, Jim Burns wrote:

On 9/7/2024 7:02 AM, WM wrote:

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Different unit fractions are different.

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Therefore there is only one the smallest one.
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They are identical because
NUF(x) counts them at the same x,

 Counting.at.x a unit.fraction.in.⅟ℕᵈᵉᶠ∩(0,x)
does not mean the unit fraction is at x

>
NUF counts only unit fractions at their positions.

Wrong! You have already stated that NUF(x) is the number of unit fractions less than the real number x. You have also stated that x is a natural number and when asked, defended that by stating that natural numbers are a subset of the reals.
Are you next going to try proving something about the naturals by going to the complex plane? The naturals are all, each, and every already defined and there is no need to extend the naturals to prove something about the naturals.
There are no Dark Numbers except in your imagination.