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

On 9/9/24 11:15 AM, WM wrote:

On 09.09.2024 16:32, Python wrote:

Le 09/09/2024 à 12:19, Prof. Dr. 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. 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.

Of course it contains aleph_0 unit fractions, but yes, 1/n isn't one of them, but you can remove any finite number of unit fractions from the set and still have aleph_0 of them.

 Note that unit fractions are points on the real line. Therefore there is a beginning. How many unit fractions can be smallerorequal than all unit fractions. This question proves the existence of a smallest unit fraction.

Nope. Try to name it.
There are NO unit fractions smaller_or_equal to ALL unit fractions, as there isn't a smallest.
Your logic is just breaking your brain.

 Regards, WM