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Chapter 3 Induction

The twin concepts of recursion and induction are fundamentally important in combinatorial mathematics and computer science. In this chapter, we give a number of examples of how recursive formulas arise naturally in combinatorial problems, and we explain how they can be used to make computations. We also introduce the Principle of Mathematical Induction and give several examples of how it is applied to prove combinatorial statements. Our treatment will also include some code snippets that illustrate how functions are defined recursively in computer programs.