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

On 9/8/2024 3:39 PM, WM wrote:

On 07.09.2024 21:01, Jim Burns wrote:

Different unit fractions are different.

>
Therefore there is only one the smallest one.

There aren't two smallest unit fractions,
and no one has said otherwise.
There isn't one smallest unit fraction because,
for each ⅟k, ⅟(k+1) disproves ⅟k being smallest.
There aren't two.
There isn't one.
There is no smallest unit fraction.

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.

strict NUFᑉ(x) ≥ NUFᑉᐧᵈᵉᶠ(x) = |⅟ℕᵈᵉᶠ∩(0,x)| does not
count any unit fraction at x.
0 < ⅟⌊2+⅟x⌋ < ⅟⌊1+⅟x⌋ < x
NUF(x) ≥ 2  ∨  NUF(x) = 0
NUF(x) ≠ 1