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

On 23.10.2024 13:37, Richard Damon wrote:

On 10/22/24 12:12 PM, WM wrote:

On 22.10.2024 18:03, Jim Burns wrote:

∀n ∈ ℕ:  2×n ∈ ℕ

>
Not if all elements are existing before multiplication already.

 IF not, then your actual infinity wasn't actually infinite

It is infinite like the fractions between 0 and 1. When doubling we get even-numerator fractions, some of which greater the 1.

Your "actual infinity" seems to be just an unimaginably large value, not infinite, as your actual infinity has an end, it has an element without a successor, so it isn't the set it claims to be.

The completed infinite cannot avoid to be complete. But it is infinite because the end cannot be determined because of the dark domain.
Regards, WM