Re: Does the number of nines increase?

Le 17/07/2024 à 05:03, Richard Damon a écrit :

On 7/15/24 8:41 AM, WM wrote:

Le 14/07/2024 à 17:27, Moebius a écrit :
 

For each and every x e IR, x > 0: NUF(x) = aleph_0

 Wrong. All unit fractions are separated. Therefore there is a first one at y. NUF(y) = 1.

 Nope.

Not all unit fractions are separated?

That means there is a highest natural number n = 1/y.

Yes.

 but m = n+1 is also a natural number,

True for definable numbers, not true for all of the ℵo dark successors
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

Your problem is you logic can't handle unbounded numbers.

Forget that magic. Explain how NUF(x) can increase from 0 to more when all unit fractions are separated. That is the crucial argument!
Regards, WM