Tree : Formal Definition
A tree T is a finite, non-empty set of nodes,
T = {r} U T1 U T2 U T3… U Tn
with the following properties:
1. A designated node of the set r, is called the root of the tree;
2. The remaining nodes are partitioned into n >= 0 subsets T1, T2, .. Tn each of which is a tree.