Sujet : Re: how
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 21. May 2024, 17:55:21
Autres entêtes
Organisation : Nemoweb
Message-ID : <vol0FSJMuqv_Uox5qeHDiF8wsA4@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 21/05/2024 à 17:50, Jim Burns a écrit :
On 5/20/2024 4:08 PM, WM wrote:
Le 19/05/2024 à 22:28, Jim Burns a écrit :
Between each pair of unit fractions,
there is a finite distance.
>
Hence
not even two unit fractions
can satisfy the condition to
sit before any x > 0.
For any x > 0
more.than.2 unit.fractions
sit before x
among them are ⅟⌊(1+⅟x)⌋ ⅟⌊(2+⅟x)⌋ ⅟⌊(3+⅟x)⌋
Of course, for any x that you can name, there are ℵo smaller unit fractions.
Ax_def > 0: NUF(x_def) = ℵo is right.
zero unit fractions sit before any x > 0
So it is!
Therefore Ax > 0: NUF(x) = ℵo is wrong.
If you forget however to distinguish between x_def and x in general, you get the contradiction:
Ax > 0: NUF(x) = ℵo is wrong.
Ax > 0: NUF(x) = ℵo is right.
Regards, WM
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