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Chapter 1 Foundations
Objectives
Recognize whether simple statements about the integers are true or false.
Give examples that illustrate true statements about the integers.
Give counterexamples for false statements.
Compute powers of integers.
Apply the properties of exponentiation.
This chapter has two purposes. It reviews basic mathematics you learned earlier and introduces the language of mathematics. We discuss statements about integers and definitions of integer properties. We introduce variables as placeholders for integers and explain how they are used in mathematics. We end with an introduction to exponentiation and its properties.
Although we work with integers in this section, the same mathematical language is used for other mathematical objects. In later chapters, we will study sets, functions, and groups.
