Re: The set of necessary FISONs

On 1/26/2025 4:33 AM, WM wrote:

On 26.01.2025 11:47, joes wrote:

Am Sun, 26 Jan 2025 10:42:48 +0100 schrieb WM:

 

{1}
{2, 1}
{3, 2, 1}
...
Can you see that the first column is not longer than all finite rows?

No.

 Crank!

Huh?
______________
0 = { 1 }
1 = { 1, 2 }
2 = { 1, 2, 3 }
3 = { 1, 2, 3, 4 }
...
______________
there are infinity many rows... Heck they are even indexed here by the unsigned integers. Starting at array index 0. Let's start at one:
______________
1 = { 1 }
2 = { 1, 2 }
3 = { 1, 2, 3 }
4 = { 1, 2, 3, 4 }
...
______________
Okay, well, what about this? lol.
______________
0 = { } // empty... can it be { 0 } ? lol.
1 = { 1, 2 }
2 = { 1, 2, 3 }
3 = { 1, 2, 3, 4 }
...
______________
Humm... It makes me think of a 2-ary tree:
______________
       0
      / \
     /   \
    /     \
   1       2
  / \     / \
.............
______________
The next level would be the children of 1 and 2:
children of 1 = (3, 4)
children of 2 = (5, 6)
?
The root is zero? Fair enough?