Sujet : Re: how
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 16. May 2024, 19:56:56
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <daccd066-734a-4138-a64a-e0766e69eadf@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 5/15/2024 9:12 AM, WM wrote:
Le 14/05/2024 à 15:35, Moebius a écrit :
Am 14.05.2024 um 13:13 schrieb WM:
Where can the first unit fractions exist
on the real line
>
Nowhere.
Since there is no such unit fraction,
it can't be anywhere.
>
Every subset of the real line has
a first element.
No.
| Assume ⅟ℕ∩(0,1] has first element ⅟G
|
| 0 < ½⋅⅟G < ⅟G < 2⋅⅟G
| There IS a unit.fraction ⅟k < 2⋅⅟G
| There is NOT a unit.fraction < ½⋅⅟G
|
| ⅟k < 2⋅⅟G exists
| (⅟k)/4 < (2⋅⅟G)/4
| ⅟(4⋅k) < ½⋅⅟G
| There IS a unit.fraction ⅟(4⋅k) < ½⋅⅟G
| Contradiction.
Therefore,
⅟ℕ∩(0,1] does NOT have a first element.