Re: because g⤨(g⁻¹(x)) = g(y) [2/2] Re: how

Le 19/04/2024 à 00:09, Jim Burns a écrit :

On 4/18/2024 10:54 AM, WM wrote:

It is enough if you explain
where ω is in the lower line:

0, 1, 2, 3, ...,   ω
|  |  |  |  |||    |
0, 2, 4, 6, ..., ω*2

 ∀κ < ω: k⋅2 < ω

That means the space between ω and ω*2 remains empty of poducts 2k, and not all natural numbers have been doubled because new products have been inserted below ω.

∀κ ≥ ω: k⋅2 > ω

But is it also less than ω*2? Are all products
{ω, ω+1, ω+2, ω+3, ...}*2 less than ω*2?
Regards, WM