Sujet : Re: how
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 21. May 2024, 16:50:44
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <881f89fb-994d-4315-b134-4aec1576bca8@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
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)⌋
zero unit fractions sit before any x > 0
| Assume otherwise
| Assume ⅟n sits before any x
|
| For xₙ = ⅟(n+1) < ⅟n
| ⅟n does NOT sit before xₙ
| Contradiction.
Therefore
Ax > 0: NUF(x) = ℵo is wrong.
for any x > 0
more.than.any.k<ℵ₀ unit.fractions
sit before x
among them are ⅟⌊(1+⅟x)⌋ to ⅟⌊(k+1+⅟x)⌋
zero unit fractions sit before any x > 0
| Assume otherwise. Contradiction.
…