4. The Formal Correspondence Definition a binary tree B is either the empty set; or consiste 数学归纳法 ot vertex v with two binary trees B1 and B2.c ray denote the binary tree with the ordered trip B=[v; B1; B2 Theorem 11.1 LS be any finite set of vertices.There is a one-to-one c rrespondence f from the set of orchards whose st t of vertices is s to the set of binary trees whose et of vertices is S Proof. Define f (o)=( Define f(V, 013, O)=[v, f(O,), f(O2)1 Show by mathematical induction on the number of vertices that fis a one-to-one correspondence4. The Formal Correspondence Definition A binary tree B is either the empty set ; or consists of a root vertex v with two binary trees B1 and B2 . We may denote the binary tree with the ordered triple B = [v;B1;B2]. Theorem 11.1 Let S be any finite set of vertices. There is a one-to-one correspondence f from the set of orchards whose set of vertices is S to the set of binary trees whose set of vertices is S. Proof. Define f () =  Define f ({v,O1 },O2 ) = [ v,f(O1 ) ,f(O2 ) ] Show by mathematical induction on the number of vertices that f is a one-to-one correspondence. 数学归纳法