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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: WM and end segments...
Date: Mon, 22 Jul 2024 14:20:48 -0700
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On 7/21/2024 1:38 PM, Chris M. Thomasson wrote:
> For some damn reason when I hear end segments from WM I think of a tree. 
> Take the following infinite 2-ary tree that holds the positive integers:
> ___________________________________________
>                    0
>                   / \
>                  /   \
>                 /     \
>                /       \
>               1         2
>              / \       / \
>             /   \     /   \
>            3     4   5     6
>           / \   / \ / \   / \
>        .........................
> ___________________________________________
[...]

To get at a parent node from any node, root 0 is "special" here...:

1 = ceil(1/2) - 1 = 0
2 = ceil(2/2) - 1 = 0

3 = ceil(3/2) - 1 = 1
4 = ceil(4/2) - 1 = 1

5 = ceil(5/2) - 1 = 2
6 = ceil(6/2) - 1 = 2

On the mirror side:

       (-1)  (-2)
          \ /
           0
          / \
       (+1)  (+2)

The parent of -1 and -2 should be zero wrt the negative side:

-1 = floor(-1/2) + 1 = 0
-2 = floor(-2/2) + 1 = 0

good. Now, the parent of say, -3 and -4 should be -1:

    (-3) (-4)
       \ /
       (-1)  (-2)
          \ /
           0
          / \
       (+1)  (+2)


-3 = floor(-3/2) + 1 = -1
-4 = floor(-4/2) + 1 = -1


the parent of -5 and -6 should be -2:

-5 = floor(-5/2) + 1 = -2
-6 = floor(-6/2) + 1 = -2


Seems to work okay, the root node is interesting here, makes me think of 
signed zero... :^)

Wrt ceil: this is right, but they are is children not its parents...

0 = ceil(0/2) - 1 = -1
0 = ceil(0/2) - 2 = -2  lol?

Humm...