Re: how

On 4/16/24 10:59 AM, WM wrote:

Le 16/04/2024 à 00:38, Richard Damon a écrit :
 

Name a Natural Number that can not be doubled!!!
>

All nameable numbers belong to a potentially infinite collection, a very small initial segment of ℕ.

>

Thus, doubling ALL the Natural Numbers still gives you results that are all Natural Numbers.

>
Impossible, since all are doubled.

>
POSSIBLE!!!!
>
That is the "miracle" of INFINITY.

 No, it is the incongruence of thinking.
For potential infinity it is true. But for actual infinity it is wrong.
 Regards, WM
 

Why?
What number in the set of Natual Numbers doesn't have another Natural Number that is twice it?
Your definitions of "Potential Infinity" and "Actual Infinity" don't seem to match what you claim they do or what they actually are.
Note, no "Natural Number" is actually infinite, that distinction falls on omega. But the SET of the Natural Numbers is Actually Infinite in Size, having a size of Aleph_0.
Does that mean the Natural Numbers themselves are individually only "Potentially Infinite" but the set of them is "Actually Infinite" by your definitions? If so, you need to be clearer about what you are talking about when you discuss things.