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

On 16.10.2024 04:45, Richard Damon wrote:

On 10/14/24 12:37 PM, WM wrote:

 

That doubling _all_ natural numbers only yields _all_ natural numbers is impossible.

 

OF course it is impossible, it only yield half of the numbers, as no odd numbers are in the set.

 There is a general truth: When doubling natural numbers we obtain natural numbers which have not been doubled.
In potential infinity we obtain more even natural numbers than have been doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.