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

On 09.09.2024 13:47, Richard Damon wrote:

On 9/9/24 6:31 AM, WM wrote:

 

And all gaps are occupied by the unit fractions. Hence every gap is
too small.

But there is always room at the bottom, where the gaps keep getting
smaller

They all are present from the start. I simply choose a gap that is too
small to contain ℵo unit fractions.

How can a claim a set of values less then a SPECIFIC NUMBER if I don't
have the number?

I claim that all unit fractions are existing as real points of the real
line. Therefore there is a first one. NUF(x) cannot increase without
passing 1 when real points are counted. Your ℵo points cannot exist
without including 1, 2, 3 first points.