Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 31.10.2024 12:36, Richard Damon wrote:

On 10/30/24 7:53 AM, WM wrote:

NUF(0) = 0, NUF(1) = ℵo. Therefore NUF must grow but cannot grow by more than 1 at any point x of the real axis.
>

Because it grows BETWEEN points on the real axis from 0 to ℵo.

I investigate its behaviour at single points.

 Your problem is there isn't a "first" x > 0 above 0 to see it increase at,

We do not see dark numbers but I can prove their existence by
∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

 so it can just jump to ℵo.

But it cannot do so at a single point.
Regards, WM