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

On 02.10.2024 14:56, joes wrote:

Am Wed, 02 Oct 2024 13:10:09 +0200 schrieb WM:

On 01.10.2024 22:05, Jim Burns wrote:

On 10/1/2024 1:29 PM, WM wrote:

>

This is incorrect:
🛇⎛ ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  shows that 🛇⎜ at no point x 🛇⎝ NUF can
increase by more than one step 1.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0  doesn't show that.

You believe that more than one unit fractions can occupy one and the
same point nevertheless? That would make the distance 0, but it is > 0.
Therefore you are wrong.

Nobody believes that. It just doesn’t follow.

It follows that either all unit fractions are at different places (then NUF grows one by one) or not. Then at least two are at the same place. There are no further alternatives.
Regards, WM