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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: WM and end segments...
Date: Sun, 21 Jul 2024 16:59:25 -0400
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After serious thinking 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
>           / \   / \ / \   / \
>        .........................
> ___________________________________________
>
> this goes on and on for infinity... We all can see how this can go for 
> infinity, right WM? Wrt trees there are only leaves in a finite view of it. 
> However, the "infinite view" of the tree has no leafs because it never 
> ends... Fair enough? Or too out there?
>
> Wrt WM, is a leaf an endsegment of an n-ary tree in your "system"? Or, I 
> probably am missing something here. Sorry everybody. Fwiw, a finite view can 
> be something like this:
> ___________________________________________
>                    0
>                   / \
>                  /   \
>                 /     \
>                /       \
>               1         2
>                        / \
>                       /   \
>                      5     6
> ___________________________________________
>
> This has leaves at 1, 5 and 6, because its finite. The infinite one has no 
> leaves. Is this a decent way to think about it? Also, if this were unit 
> fractions, the root at zero is not a unit fraction. So, zero is not valid in 
> that strict realm. For instance wrt the finite view above:
>
> ___________________________________________
>                  (1/0)  *** NOT A UNIT FRACTION!
>                   / \
>                  /   \
>                 /     \
>                /       \
>              (1/1)    (1/2)
>                        / \
>                       /   \
>                     (1/5) (1/6)
> ___________________________________________
>
>
> Sound okay, or into kook ville! ;^o

It is kind of like that. WM would say that each 'level' as you build it 
step by step has twice as many leaf nodes as the previous level. More 
and more and more. Then, when it is infinite, suddenly there are no 
leaf nodes. What happened, he ponders.

Then you start smelling smoke...