Re: how

On 5/22/2024 3:13 PM, WM wrote:

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.

Therefore,
you are not correct.

>
I am. It is 0.

0 is the greatest lower bound of unit fractions.
There is no x > 0 smaller than all unit fractions.
¬∃ᴿx > 0: ∀¹ᐟᴺ ⅟k: x ≤ ⅟k
For any x > 0
there is a unit.fraction ⅟n₁ < x
there is a unit.fraction ⅟n₂ < ⅟n₁
there is a unit.fraction ⅟n₃ < ⅟n₂
...
there is a unit.fraction ⅟nₖ₊₁ < ⅟nₖ
For any x > 0
there are more.than.any.k<ℵ₀ unit.fractions < x

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.

For any x > 0
there are more.than.any.k<ℵ₀ unit.fractions < x