Re: how

Le 22/05/2024 à 20:58, Jim Burns a écrit :

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.

One of them is zero.

|
| 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.

I am. It is 0.
But your "proofs" are nonsense. Disprove this: Between ℵo unit fractions there are at least ℵo real numbers x. For them NUF(x) = ℵo is wrong.
Regards, WM