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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: WM and end segments...
Date: Sun, 21 Jul 2024 13:38:27 -0700
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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