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

Le 07/09/2024 à 15:03, WM a écrit :

On 07.09.2024 14:37, Richard Damon wrote:

On 9/7/24 8:04 AM, WM wrote:

 

NUF(x) changes by 1 because a change by more at any x would count more different unit fractions 1/n,  1/m, 1/k, ... which are identical because they are the same x = 1/n = 1/m = 1/k = ... .
>

And thus is always has a value of aleph_0 for all x > 0, since there is always aleph_0 unit fractions below and finite positive x value.

 Stop that nonsense. ℵo unit fractions cannot fit into every interval (0, x).

Of course they can.
"There's Plenty of Room at the Bottom" — Richard Feynman.

The distance between two unit fractions already is larger.

Some are, but for ℵo pairs of them they be arbitrary small
(i.e. < x).
How can you be so wrong on such elementary stuff Crank Mückenheim?