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

On 03.09.2024 06:25, Jim Burns wrote:

On 9/2/2024 4:37 PM, WM wrote:

On 02.09.2024 19:19, Richard Damon wrote:

 

as any unit fraction you might claim to be
that one has a unit fraction smaller than itself,
so it wasn't the smallest.

>
Your argument stems from visible unit fractions
but becomes invalid in the dark domain.

 The darkᵂᴹ domain
  between 0 and visibleᵂᴹ unit.fractions
is empty.

Then you could see the smallest unit fraction. Remember that they are fixed points with non-empty gaps on the real line. Hence there is a first one.

 Each positive point is undercut by
visibleᵂᴹ unit.fractions,

No. Only each visible positive point is undercut by
visible unit.fractions.

⎛ Assume otherwise.

Assume that there is no first unit fraction. The alternative would be more first unit fractions, i.e., real nonsense.

The unit fractions end before zero.

 The lower.end of unit fractions
is not.

Then NUF(x) would remain at 0. It does not.
Regards, WM