Re: how

Le 19/04/2024 à 00:42, Richard Damon a écrit :

On 4/18/24 10:59 AM, WM wrote:

 ω follows upon all natural numbers. There is nothing between them and ω.

Right, and any Natural Number * 2 is a Natural Number, so less than ω.

If all elements of the set {1, 2, 3, ...} are doubled and nevertheless remain below ω, then you have created new natural numbers which have not been doubled. Hence you have not doubled all natural numbers. But that is what has to be done and, according to actual infinity, can be done.

 Your logic can't handle the fact that the set of Natural  Numbers is unbounded on the high side, so it doesn't understand that.

Your logic can't double all natural numbers such that none below ω is missing. You create always new natural numbers. They have  not been doubled.
Regards, WM