TABLE OF CONTENTS In this chapter we introduce relations, functions and various notations connected with functions, and study some basic concepts intimately related to functions.
In mathematics it is customary to define new concepts by using set theory. To say that two things are related is really the same as saying that the ordered pair (a, b) has some property. This, in turn, can be expressed by saying that the pair (a, b) belongs to some set. We define:
A relation is a set of ordered pairs.
This means that if A and B are sets then a relation is a part of the cartesian product A B. If a set R is a relation and ( a, b) ? R then the elements a and b are related; we also denote this by writing aRb. For example, if related means that the first person is the father of the second person then this relation consists of all pairs of the form (father, daughter) or (father, son). Another example of a relation is the set C={(1, 2), (2, 3), , (11, 12), (12, 1)}. This relation can be interpreted by saying that m and n are related (mCn) if n is the hour immediately following m on the face of a 12 hour clock.
We define the domain of the relation R to be the set of...
