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

On 9/27/2024 3:13 PM, FromTheRafters wrote:

WM expressed precisely :

On 25.09.2024 19:22, Richard Damon wrote:

On 9/25/24 11:14 AM, WM wrote:

NUF increases. At no point it can increase by more than 1.

>
Why not?

>
Because there is a finite gap between two unit fractions.

 There are no gaps in the set of unit fractions.

He might be thinking of the gap between say 1/1 and 1/2, its there. Think of the "granularity" of _strict_ unit fractions for a moment.
Then think of trying to fill the gap with unit fractions breaking the strict rule for sure:
1/2 + ((1/16*4 + 1/8*3 + 1/4 + 1/8) - 1/2) = 1
;^)