Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 09. Sep 2024, 16:15:23
Autres entêtes
Organisation : A noiseless patient Spider
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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.
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.
Regards, WM
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