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

On 10/12/24 2:39 PM, WM wrote:

On 11.10.2024 20:02, Jim Burns wrote:
 

"Potential ℕ" vs. "actual ℕ" leaves unchanged
which claims we reason to.

 Potential infinity: All natural numbers when double yield natural numbers but larger numbers are among the result.
In actual infinity no new naturals can be created but since doubling doubles the value of each number, numbers of the second number class are created.
 Regards, WM

No, in actual infinity no new natural can be created, but every natural number can find the one that is twice itself in the set, they are all there because they were created in the infinite creation process.
No new number need to be created, becuase the set was ACTUALLY infinite.
The fact that doesn't make sense to you is because you haven't learned how to handle the logic of INFINITE sets, which act somewhat differently than the finite sets, in part because we can not actually observe an actually infinite set.
It seems your idea of "actual infinity" is a set that was taken BEFORE we got to the actual infinity (because you just can't handle actual infinity) and thus it isn't actually infinity, just some really big set, whch isn't infinity.