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

On 01.10.2024 22:05, Jim Burns wrote:

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

>

>
What is incorrect?

 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.

 ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  shows
∀n ∈ ℕ: 1/n  >  1/(n+1) > 0
which shows
each unit fraction 1/n is not first.

>
No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 does not prove that n+1 is a natural number. Note the infinite sequence
1, 2, 3, ..., ω-2, ω-1, ω.