Why Read This Book? - Index of

Sets and Their Properties
3
All of the results in Chapter 2 were about familiar sets of numbers, in particular
their algebraic properties arising from the binary operations of addition and multiplication.
This chapter will also address properties of real numbers, but within a
broadened context of their familiar subsets (N, W, Z, and Q) and sets in general.
3.1 Set Terminology
First, we return to the set terms from Chapter 0 and introduce several others.
Given a set A in the context of a universal set U, we often illustrate with a Venn
diagram, as in Figure 3.1. Shading a Venn diagram can sometimes be helpful to
illustrate sets under discussion.
Definition 3.1.1 Given a set A, we define the complement of A, denoted AC the following way.
,in
A C ={x : x ∈ U and x/∈ A} (3.1)
Thus x ∈ A C if and only if x/∈ A. See Figure 3.2.
Given two sets A and B, a general Venn diagram would look like that in
Figure 3.3. We can now define several important binary operations to create new
sets from A and B.
Figure 3.1 Basic Venn diagram.
U
A
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