ABSTRACT

This chapter explores both mathematical induction and strong mathematical induction. A perusal of Gunderson’s Handbook of Mathematical Induction provides a glimpse at just how powerful of a tool mathematical induction truly is. It should be noted that the Principle of Mathematical Induction is applicable not just to predicates whose domain is the set of all positive integers. The chapter discusses how they can be used to prove a variety of number theoretic results. Mathematical induction is a proof technique that can be used in a variety of contexts. The next few results serve to show its versatility, with the first being used to prove an inequality. The chapter examines various major theorems: the Binomial Theorem, the Fundamental Theorem of Arithmetic and Euclid’s Lemma. Mathematical induction seems like a natural choice for a proof technique; the sequence is defined recursively, so assuming something is true about a previous term may lead to information about the next term.