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

On 10/16/24 1:53 PM, Chris M. Thomasson wrote:

On 10/16/2024 4:54 AM, Richard Damon wrote:

On 10/16/24 4:27 AM, WM wrote:

On 15.10.2024 02:00, Jim Burns wrote:
>

So, what is that perfectly reasonable explanation?

>
There is a general rule not open to further discussion:
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.
>
Regards, WM

>
But that isn't actually a general rule, so you are just admitting that you aren't talking about the same Natural Numbers that everyone else is talking about, but some bastadization that is just fininte.
>
NO natural number when doubled results in a value that wasn't a natural number all the time.

>
Humm. Don't tell me WM thinks that 2 is not a natural because 1*2=2

 He seems to think there exists Natural Numbers, in the Actually Infinite set where they are exist for all time and never change, that when double get you to a number that wasn't in that set.
 But since the result IS a Natural Numbers, it must have been, or is "actual infinity" didn't actually contain *ALL* the Natural Numbers.