In this lesson on mathematical induction, we learn about the stronger version of the principle called the principle of strong mathematical induction. This principle allows for the proof of propositions that may not be valid for all natural numbers. An example of a proposition that can be proved with strong induction is that any natural number greater than one is prime or the product of primes. Additionally, Fermat's method of infinite descent is introduced as a variant of the principle of mathematical induction, and it is used to prove that the square root of 2 is irrational. Finally, the well ordering principle is presented as an axiom, which is equivalent to the principle of mathematical induction.
Learn about strong mathematical induction, the well ordering principle, and Fermat's method of infinite descent. Two famous proofs are also presented.