Re: how

On 4/23/24 3:51 PM, WM wrote:

Le 23/04/2024 à 21:45, Tom Bola a écrit :

WM schrieb:
>

Le 23/04/2024 à 01:01, Richard Damon a écrit :

On 4/22/24 10:15 AM, WM wrote:

>

The results cannot be compressed to the interval (0, ω) of the set { 1, 2, 3, ...}. This shows that new numbers are generated by multiplication.
>

Of course they can be compressed into the interval (0, ω), as every finite number n < ω, when doubled results in a finite number 2n which is also < ω.

>
Try to map the closed interval [0, ω]*2 = [0, ω*2].

>
f = (0, 0),
(1, 2),
(2, 4),
(3, 6),
(..., ...),
(w, w*2)

 Indeed. When n reaches ω, 2n reaches ω2.
 Regards, WM

But n, the finite number, never reaches ω.
ω isn't just some unimaginably big number, it is a value beyond finiteness, a transfinite value, and infinity.
Of course, if you logic tries to make that transfinite value finite because that is all it can handle, your system just blows up in your face.