Introduction to Trees

The article consists of two parts: the first one deals with the concept of the prefixes of a finite sequence, the second one introduces and deals with the concept of tree. Besides some auxiliary propositions concerning finite sequences are presented. The trees are introduced as non-empty sets of finite sequences of natural numbers which are closed on prefixes and on sequences of less numbers (i.e. if 〈n1, n2, . . ., nk〉 is a vertex (element) of a tree and mi ≤ ni for i = 1, 2, . . ., k, then 〈m1, m2, . . ., mk〉 also is). Finite trees, elementary trees with n leaves, the leaves and the subtrees of a tree, the inserting of a tree into another tree, with a node used for determining the place of insertion, antichains of prefixes, and height and width of finite trees are introduced.