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

Am 09.09.2024 um 17:27 schrieb Python:

Le 09/09/2024 à 17:15, Crank Mückenheim, aka WM a écrit :

On 09.09.2024 16:32, Python wrote:

Le 09/09/2024 à 12:19, Crank Mückenheim, aka WM a écrit :

>

ℵo unit fractions cannot fit into one of the ℵo intervals between two of them.

>
(O, x) is NOT an interval between two unit fractions.

>
1/n - 1/(n+1) = x is an interval between two unit fraction. [WM}

 No. It is a number.

Right. Actually, it's a unit fraction! :-)
| x = 1/k - 1/(k+1) = 1/[k*(k+1)] > 0
Hence x =  1/[k*(k+1)] e {1/n : n e IN}.

This interval is shifted to the origin, yielding the interval (0, x). It does not contain ℵo unit fractions. It does not contain 1/n.

 1/n is not in (0, x). Sure. So what? Nevertheless there are Aleph_0 unit
fractions in (0, x). No need for 1/n to be there, there far enough other
fractions.

Right, for example the infinitely many unit fractions 1/(1/x + 1), 1/(1/x + 2), 1/(1/x + 3), ...
:-P
What a crank. "Teaching" at a "Hochschule". <facepalm>