Re: how

On 5/22/2024 1:57 PM, WM wrote:

Le 22/05/2024 à 17:48, Jim Burns a écrit :

There is no x > 0 smaller than all unit fractions.
¬∃ᴿx > 0: ∀¹ᐟᴺ ⅟k: x ≤ ⅟k

>
There is an x >= 0 smaller than all unit fractions.

| Assume you are correct.
| Assume that there is
| an x ≥ 0 smaller than all unit fractions.
|
| There are points 2⋅b¹ᐟᴺ > ½⋅b¹ᐟᴺ > 0
| such that
| Unit.fraction ⅟k < 2⋅b¹ᐟᴺ
| No unit.fraction < ½⋅b¹ᐟᴺ
|
| ⅟k < 2⋅b¹ᐟᴺ
| (⅟k)/4 < (2⋅b¹ᐟᴺ)/4
| ⅟(4⋅k) < ½⋅b¹ᐟᴺ
| Unit.fraction ⅟(4⋅k) < ½⋅b¹ᐟᴺ
| Contradiction.
Therefore,
you are not correct.