208CHAPTER13 Mappings, Relations, and Functions
When the elements of two sets are associated with each other in an organized way, the asso-
ciation is called a mapping. When the set elements are numbers, a mapping is often called
arelation. A function is a relation that has special characteristics about which you’ll learn in
this chapter.Mapping “Territories”
Imagine two sets of points, defined by the shaded rectangles in Fig. 13-1. Suppose you’re
interested in the subsets shown by the hatched ovals. You want to match the points in the top
oval with those in the bottom oval by means of a defined scheme. When you do this, you map
the elements of one set to the elements of the other set.Point matching
Think of Fig. 13-1 as portraying two vans carrying people, some of whom are using cell
phones to send or receive text messages. The people in one van (call it the upper van) are
represented by all the points inside the top rectangle, and the people in the other van (call
it the lower van) are represented by all the points inside the bottom rectangle. Within each
van, the people involved in cell-phone “texting” are represented by points inside the ovals.
The arrows indicate the direction of the mapping—in this case, the direction in which
messages are sent.Domain and range
All the points actively involved in the mapping shown by Fig. 13-1 are inside the ovals. The
top oval is called the domain of the mapping. Sometimes it’s called the essential domain. The
bottom oval is called the range. Here, the domain contains six points, and the range contains
five points. In this example, the domain of the mapping is exactly the set of people in the
upper van who are sending messages. The range is exactly the set of people in the lower van
who are receiving messages.Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.