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

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

On 03.09.2024 19:50, Jim Burns wrote:
 > On 9/3/2024 6:22 AM, WM wrote:
  > If the smallest unit.fraction existed,
 > you could see it
No, that is impossible by your argument:
  > positive and undercut by
 > a visibleᵂᴹ smaller.than.smallest unit.fraction.
 >
 > But you can't see that.
 > The smallest unit fraction doesn't exist.
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.
 Regards, WM

And all ARE different as there is always a space between them, but that space gets arbitrary small (but still finite.)
You just can't seem to handle the concept of ARBITRARILY small, and think you can somehow "name" that.
That naming is a property of FINITE sets, not unbounded sets.