Chapter 1

Logical Thinking

Mathematicians are in the business of stating things precisely. When you read a mathematical statement, you are meant to take every word seriously; good mathematical language conveys a clear, unambiguous message. In order to read and write mathematics, you must practice the art of logical thinking. The goal of this chapter is to help you communicate mathematically by understanding the basics of logic.

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Figure 1.1 Symbols are an important part of the language of mathematics.

A word of warning: mathematical logic can be difficult—especially the first time you see it. This chapter begins with the study of formal, or symbolic, ...

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