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

Le 28/04/2024 à 19:29, Jim Burns a écrit :

On 4/27/2024 10:46 AM, WM wrote:

If n can be counted to from 0
then n⋅2 can be counted to _from n_
then n⋅2 can be counted to from 0 _through n_

That is true.

If n is before ω
then n⋅2 before ω

That is not true.

 However,
it is always true that,
if n is before ω
then n⋅2 before ω

No.

My guess is that you (WM) feel

Whatever you guess, {1, 2, 3, ..., ω}*2  results in {2, 4, 6, ..., ω*2}. ω or ω+1 is amidst, neither near the left border nor near the right border. Everything else is crippled mathes.
Regards, WM