Re: how

Le 22/05/2024 à 01:27, Jim Burns a écrit :

On 5/21/2024 12:55 PM, WM wrote:

for any x > 0

that you can determine

more.than.any.k<ℵ₀ unit.fractions
sit before x
among them are ⅟⌊(1+sₓ/rₓ)⌋ to ⅟⌊(k+1+sₓ/rₓ)⌋
 

Ax_def > 0: NUF(x_def) = ℵo is right.

 ∀x ∈ ℝ: x > 0 ⇒ NUF(x) = ℵ₀

If there is no unit fraction smaller than all x > 0, then there is an x > 0 preventing this.
That is merciless logic.

 

zero unit fractions sit before any x > 0

 So it is!
Therefore Ax > 0: NUF(x) = ℵo is wrong.

 No. Your "therefore" is a quantifier shift.

There is no shift but merciless logic!
Your quantifiers cannot be an excuse for not understanding logic.
Zero unit fractions sit before any x > 0. What prevents this? That can only be accomplished by an x without smaller unit fractions.
Regards, WM