ABSTRACT

The principle of mathematical induction will give a general approach to obtaining proofs of statements. This chapter establishes some of the concepts necessary to formulate and explore a wider range of questions. It provides proofs for the principle of mathematical induction and uses the principle of mathematical induction to prove useful generalization prepositions. The principle of mathematical induction can be thought of as a statement about the natural numbers. It turns out to be equivalent to another statement about the natural numbers called the well-ordering principle. The chapter proves that the well-ordering principle and the strong principle of mathematical induction are equivalent. It also includes some exercise problems related to the concepts discussed.