Sets, Relations, And Functions

Sets are fundamental in mathematics. In this chapter we briefly introduce the concepts and notations from set theory we will use throughout the book. We assume that the reader is familiar with the basic concepts of set theory. He may use some kind of naive set theory or a formal theory as ZF or ZFC [18], i.e., the Zermelo-Fraenkel axioms of set theory. As usual, we denote the fact that “x is an element of a set A” by x ∈ A. The set with no elements is called the empty set, and is denoted by ∅. If every element of a set A is also an element of the set B, we say A is a subset of B denoted by A ⊆ B.