Re: how

On 4/25/2024 1:20 PM, WM wrote:

Le 25/04/2024 à 01:13, Richard Damon a écrit :

On 4/24/24 1:16 PM, WM wrote:

Le 24/04/2024 à 04:01, Richard Damon a écrit :

On 4/23/24 3:34 PM, WM wrote:

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].
If [0, ω) --> [0, ω) and ω*2 --> ω*2, then ω*2 is the only image point in (ω, ω*2]. Infinitely many points remain empty. Crippled mathematics. Ugly. Inacceptable.

>

Why?

>
Continuity.

>
Who says we have that sort of "Continuity"?

 I.
 If the preimage has intervals of 1, then the image has intervals of 2.

A =       { 1, 2, 3, 4, ... }
A*2 =     { 2, 4, 6, 8, ... }
(A*2)/2 = { 1, 2, 3, 4, ... }
There is a one-to-one direct mapping back and fourth and both sets are infinite. They have the same size...

 ω+n is existing. How is it approached if not from the finite domain?
 Regards, WM