>>11 You prove the correctness of a function be first proving all of the calls it makes yield correct results
No.
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (positive integers). It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one. -- http://en.wikipedia.org/wiki/Mathematical_induction
Please get out and study for a while before posting again.