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

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.

∀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.
It consists of infinitely many finite numbers.

Those last numbers are not finite, and this is not a sequence (it is
not connected). Your favorite triviality presupposes a natural n+1.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.