Patch to the solution for HW 8, problem 5 ========================================= This proof actually needs a second base case, for n=3, because the inductive step is referencing results for the previous two smaller trees. The extra base case would say that T_3 consists of a root plus two edges, so it has height 1, which is equal to n-2. There may be ways to avoid the second base case by adding some additional discussion to the inductive step, or by first arguing that T_k+1 is always at least as tall as T_k. But we think adding the second base case is the most elegant method.