In This Chapter
Defining a set and its elements
Understanding subsets and the empty set
Knowing the basic operations on sets, including union and intersection
A set is just a collection of things. But in their simplicity, sets are profound. At the deepest level, set theory is the foundation for everything in math.
Set theory provides a way to talk about collections of numbers, such as even numbers, prime numbers, or counting numbers, with ease and clarity. It also gives rules for performing calculations on sets that become useful in higher math. For these reasons, set theory becomes more important the higher up you go the math food chain — especially when you begin writing mathematical proofs. Studying sets can also be a nice break from the usual math stuff you work with.
In this chapter, I show you the basics of set theory. First, I show you how to define sets and their elements and how you can tell when two sets are equal. I also show you the simple idea of a set's cardinality. Next, I discuss subsets and the all-important empty set (∅). After that, I discuss four operations on sets: union, intersection, relative complement, ...