Re: how

Le 17/04/2024 à 01:29, Richard Damon a écrit :

On 4/16/24 2:36 PM, WM wrote:

Le 16/04/2024 à 18:38, Mike Terry a écrit :

On 16/04/2024 16:05, WM wrote:

Le 16/04/2024 à 02:35, Mike Terry a écrit :

On 15/04/2024 14:00, Tom Bola wrote:

>

0, 1, 2, 3, ...,   w,   w+1,   w+2,   w+3, ...     w+w
|  |  |  |  |||    |     |      | |            |
0, 2, 4, 6, ..., w*2, w*2+2, w*2+4, w*2+6, ... w*2+w*2

>
Should be:
>
0, 1, 2, 3, ...,   w,   w+1,   w+2,   w+3, ...     w+w
|  |  |  |  |||    |     |      | |            |
0, 2, 4, 6, ..., w*2, w*2+1, w*2+2, w*2+3, ... w*2+w*2

>
No. (ω+1)*2 = ω*2 + 2

>
No, you need to learn how ordinal arithmetic works:
>

I see: 1 + ω = ω.
 Nevertheless the question remains where in the second row is ω located, doesn't it?.
 

Why does it need to be there?

Because ω is smaller than ω2.

 THe two set/series are of the same size even though the bottom misses the "odd" values.

The two sets are of same number of elements because every elements is doubled. But after multiplication these elements cover an interval twice as large as before. The end is ω2. Therefore ω or its neighbours are located in the midst of the interval.
Regards, WM