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

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 : { 1/p : p > k*(k+1) } has cardinal ℵo,
contains only unit fractions, and is a subset of (0, x)
Ask one of your "students" if you don't understand, crank.