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

On 01.10.2024 01:07, Richard Damon wrote:

On 9/30/24 2:54 PM, WM wrote:

NUF(0) = 0 and NUF(1) = ℵo. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 shows that at no point x NUF can increase by more than one step 1. It is fact with your set too. I am not responsible. I only made the discovery.

 Actually, it shows that at no point CAN it increase by 1.

Wrong because it cannot start with ℵo.

 For any finite number x, NUF(x) will be Aleph_0, and Aleph_0 when you attempt to "increment" it, doesn't change.

If NUF is ℵo at all x > 0 then it must count ℵo unit fractions at 0. Wrong.

 Since there is no finite value of x where NUF(x) can be 1

Wrong presupposition.
Regards, WM