Recursive Definitions Definition A rooted tree consists of a single vertex V, called the root of the tree, together with a forest F whose trees are called the subtrees of the root A forest F is a (possibly empty) set of rooted trees Definition An ordered tree T consists of a single vertex v, called the root of the tree, together with an orchard o whose trees are called the subtrees of the root v We may denote the ordered tree with the ordered pair T=vON An orchard o is either the empty set ;, or consists of an ordered tree T, called the first tree of the orchard, together with another orchard o(which contains the remaining trees of the orchard). We may denote the orchard with the ordered pair O=(T, O).Recursive Definitions Definition A rooted tree consists of a single vertex v, called the root of the tree, together with a forest F , whose trees are called the subtrees of the root. A forest F is a (possibly empty) set of rooted trees. Definition An ordered tree T consists of a single vertex v, called the root of the tree, together with an orchard O,whose trees are called the subtrees of the root v. We may denote the ordered tree with the ordered pair T = {v,O}. An orchard O is either the empty set ;, or consists of an ordered tree T , called the first tree of the orchard, together with another orchard O’ (which contains the remaining trees of the orchard). We may denote the orchard with the ordered pair O = (T ,O’)