Re: how

On 5/13/2024 4:15 PM, WM wrote:

Le 10/05/2024 à 16:21, Moebius a écrit :

Ax > 0: NUF(x) = ℵo.

⎛ ∀x > 0: NUF(x) = ℵ₀
⎝ ¬∃x > 0: NUF(x) < ℵ₀
0 ≤ NUF(x) ≤ ℵ₀ ∉ ℕ

Then there would sit
ℵo unit fractions before any x > 0,
that is at x = 0.

No.
kₓ = ⌊⅟x⌋
⌊⅟x⌋-1 < ⅟x ≤ ⌊⅟x⌋ ∈ ℕ
⎛⎛ ∀x > 0:
⎜⎜⎛ ∀n ∈ ℕ⁺
⎜⎜⎜ [!]  0 < ⅟kₓ⁺ⁿ < ⅟kₓ ≤ x
⎜⎝⎝ NUF(x) > n
⎜
⎜⎛ ¬∃x > 0:
⎜⎜⎛ ¬∃n ∈ ℕ⁺
⎜⎜⎝ NUF(x) ≤ n
⎝⎝ NUF(x) < ℵ₀
⎛ ¬∃x > 0: NUF(x) < ℵ₀
⎝ ∀x > 0: NUF(x) = ℵ₀

Wrong.
No unit fraction sits at x = 0.
Try again.