The Well-Ordering Principle

The well-ordering principle is a concept which is equivalent to mathematical induction. In your textbook, there is a proof for how the well-ordering principle implies the validity of mathematical induction. However, because of the very way in which we constructed the set of natural numbers and its arithmetic, we deduced, in class, the validity of mathematical induction directly from the axioms of set theory. In this note, we show how mathematical induction, in turn, implies the well-ordering principle.