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

Le 05/09/2024 à 02:35, Richard Damon a écrit :

On 9/4/24 3:10 PM, WM wrote:

Either ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is wrong or Peano is wrong.

 Why?
 

Peano has been generalized from the small natural numbers.
"All different unit fractions are different" however is a basic truth. Therefore I accept the latter.

 And all ARE different as there is always a space between them, but that space gets arbitrary small (but still finite.)

NUF(x) increases from 0 to ℵo. But it cannot increase to ℵo at one point x > 0 because at every point there is at most one unit fraction.  .Before ℵo there come 1, 2, 3, ...
Regards, WM