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

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

On 08.09.2024 22:34, Python wrote:

Le 08/09/2024 à 21:28, Crank Mückenheim, aka WM a écrit :

On 07.09.2024 16:05, Python wrote:

Le 07/09/2024 à 15:03, WM a écrit :

>

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

>
Of course they can.

>
Select any gap between one of the first ℵo unit fractions and its neighbour. Call its size x.

>
x = 1/k - 1/(k+1) = 1/[k*(k+1)] > 0
>

Then ℵo unit fractions cannot fit into the interval (0, x), independent of the actual size.

>
It can and it does

 Nonsense. 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. It has, anyway,
the same length that another interval that is between two neighboring
unit fractions.
Ask one your students^H^H^H^H^H^H^H^H^H victims. They know better
than you.