Chapter 2
Sets, Numbers, and Axioms
Set theory is the language within which mathematics is communicated. In this chapter, we introduce this language, including standard set-theoretic terminology and notation, and apply it while exploring various kinds of numbers. We also take our first look at the axiomatic approach to mathematics by establishing some foundational assumptions that reflect our intuition about sets and numbers.
2.1 Sets and Numbers from an Intuitive Perspective
Questions to guide your reading of this section:
1. How can listing be used to describe a set? What is the significance of the ellipsis notation (…)?
2. How can we symbolically indicate that a certain object is a member of a particular set?
3. Which numbers are ...
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