# Methods of Proof

• Răzvan Gelca
• Titu Andreescu
Chapter

## Abstract

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).

## Keywords

Positive Integer Prime Number North Pole Multiplicative Function Mathematical Induction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

• Răzvan Gelca
• 1
• Titu Andreescu
• 2
1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
2. 2.School of Natural Sciences and MathematicsUniversity of Texas at DallasRichardsonUSA