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

On 02.10.2024 23:06, Jim Burns wrote:

On 10/2/2024 7:10 AM, WM wrote:

 You (WM) believe in quantifier shifts,
the opposite of that.

I believe that if every n that can be chosen has ℵ₀ successors, then all n that can be chosen have ℵ₀ successors. Proof by your inability to contradict this.

 

You believe that
more than one unit fractions
can occupy one and the same point
nevertheless?

 No.

Then NUF can increase at every point by at most 1.

1, 2, 3, ..., ω-2, ω-1, ω

 ...is a _finite_ sequence.
As you have written it,
ω and each non.0 α < ω has a predecessor,
which makes ω finite.

The predecessors in the dark realm cannot be known. You can subtract every natural number from ω without traversing the dark realm. You can add every natural number to every natural number without traversing the dark realm. That is the essence of infinity!
Regards, WM