On Feb 21, 2008, at 1:00 AM, John F. Sowa wrote:
> Dear Matthew, Pat, Chris, and Ed,
>
> Since other people have responded very well, I'd just like to
> comment on one point:
>
> CM> ... in fact, you can define a tree to be a connected acyclic
> graph.
>
> That is only true for undirected trees ... (01)
Quite right, I accessed the wrong memory address there. :-) For
directed trees (which were the only kind that made sense in the
context) one has to include the unique immediate predecessor condition
Pat mentioned. The more formal definition in set theory is that a
tree is a partially ordered set (T,<) such that set of the
predecessors of any given node is well-ordered by <. This definition
permits trees to have more than one root, but that could of course be
ruled out by a further condition. (02)
Intuitively, the idea is that, in a tree (with a single root), there
is a unique, discrete path from the root node to any other node in the
tree. (This of course entails the unique immediate predecessor
condition.) (03)
-chris (04)
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