In this introductory chapter we explain some methods of mathematical proof. They are argument by contradiction, the principle of mathematical induction, the pigeonhole principle, the use of an ordering on a set, and the principle of invariance.
The basic nature of these methods and their universal use throughout mathematics makes this separate treatment necessary. In each case we have selected what we think are the most appropriate examples, solving some of them in detail and asking you to train your skills on the others. And since these are fundamental methods in mathematics, you should try to understand them in depth, for “it is better to understand many things than to know many things” (Gustave Le Bon).
KeywordsPositive Integer Prime Number North Pole Multiplicative Function Mathematical Induction
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