please help

Problem 6 (Extra Credit 1 point). The following statement is called the well ordering principle. Any nonempty subset of N has a smallest element. In class, we have introduced mathematical induction and we have taken as an axiom, that mathematical induction works (this is called the principle of mathematical induction). It turns out that the well ordering principle is equivalent to the principle of mathematical induction and so we could have instead taken the well ordering principle as one of our axioms and proved that induction works using the well ordering principle. For this problem, use mathematical induction to prove the well ordering principle. Hint: Let S C N. You need to prove that S has a smallest element. Do so by proving the contrapositive "if S doesn't have a smallest element, then S =0". Thus, you should begin by assuming that S doesn't have a smallest element. Then, prove S must be empty by proving "for every natural number n, the numbers from 0 to n are not in S" using induction