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

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

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

Le 18/04/2024 à 00:50, Jim Burns a écrit :

On 4/16/2024 10:33 AM, WM wrote:

Le 15/04/2024 à 23:06, Jim Burns a écrit :

On 4/15/2024 7:59 AM, WM wrote:

 

That is wrong if
all natnumbers are present already such that
no further natnumbers fits below ω.

 

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

0, 1, 2, 3, ...,   w  = X
|  |  |  |  |||    | 0, 2, 4, 6, ..., w*2  = Y

>
Please answer the question.

 | Set X fits set Y

Yes both sets have the same number of elements. But the interval covered by Y is twice as large as that covered by X.

 | X and Y are same.sized
| X [=] Y
  is a claim that
  a function exists 1.to.1.onto.from.to:#

The question was: Where in the second line sits ω?
Sorry, I could not find the symbol ω in your text. I assume you deny to answer because the answer would prove you wrong.
Regards, WM