WM and end segments...

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