CHAPTER 9

Induction

9.1 INTRODUCTION

Induction is reasoning from the specific to the general. If various instances of a schema are true and there are no counterexamples, we are tempted to conclude a universally quantified version of the schema.

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Incomplete induction is induction where the set of instances is not exhaustive. From a reasonable collection of instances, we sometimes leap to the conclusion that a schema is always true even though we have not seen all instances. Consider, for example, the function f where f(1) = 1, and f(n + 1) = f(n) + 2n + 1. If we look at some values of this function, we notice a certain regularity—the value of

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