Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : python (at) *nospam* invalid.org (Python)
Groupes : sci.mathDate : 08. Sep 2024, 22:34:01
Autres entêtes
Organisation : CCCP
Message-ID : <vbl1nq$21t3j$3@dont-email.me>
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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.
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