Re: how

On 4/19/24 11:39 AM, WM wrote:

Le 19/04/2024 à 00:40, Richard Damon a écrit :

On 4/18/24 11:08 AM, WM wrote:

Le 18/04/2024 à 01:27, Phil Carmody a écrit :

Richard Damon <richard@damon-family.org> writes:

>

That means that YOUR logic system is proven INCONSISTENT, and thus
BLOWN UP.

>
And that is where the intrigue lies.

>
My logic system says: ω is amidst the interval (0, ω2) because in the image of the function f(x) = x*2 there are as many ordinals in (ω, ω2) as in (0, ω).
>

>
And if your logic doesn't understand that the "ordinals" in (ω, ω*2) are different than those of (1, 2, 3, ...) it is just broken.

 Of course they are different since all those of (1, 2, 3, ...) have been doubled and therefore cannot remain the same set.

Nope, sjnce every natural number has aleph_0 natural numbers after it, they are never "used up", but there are always more.
Your logic just breaks on unbounded sets.

>
Any finite number *2 will be less than ω.

 Not if all those which could emerge from doubling are doubled too.

Yep, since you can't "use up" an infinte set that way.

 Regards, WM