Re: how

WM schrieb:

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.

I forgot the surrounding brackets {}...

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

If you want something else *you* are (the one) to define it.