High Quality Content by WIKIPEDIA articles! In set theory, a tree is a partially ordered set (poset) (T, <) such that for each t ? T, the set {s ? T : s < t} is well-ordered by the relation <. For each t ? T, the order type of {s ? T : s < t} is called the height of t (denoted ht(t, T)). The height of T itself is the least ordinal greater than the height of each element of T. A root of a tree T is an element of height 0. Frequently trees are assumed to have only one root (as the typical questions that are investigated in this field are easily reduced to questions about single-rooted trees).Trees with a single root in which each element has finite height can be naturally viewed as rooted trees in the graph-theoretical sense: there is an edge from x to y if and only if y is a direct successor of x (i.e., x<y, but there is no element between x and y). However, if T is a tree of height > ?, then there is no natural edge relation that will make T a tree in the sense of graph theory.

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