Algebra Know-It-ALL

210 Mappings, Relations, and Functions

that contains two items separated by a comma. The first item represents an element of the

domain. The second element represents an element of the range. In the situation shown by

Fig. 13-1, the ordered pairs are (a,v), (b,w), (c,v), (c,x), (c,z), (d,y), (e,z), and (f,y). When you

write an ordered pair, you can (but don't have to) put a space after the comma, as you would

in an ordinary sequence or a list of set elements.

Are you confused?

In the example of Fig. 13-1, the correspondence between the points in the domain and the points in the

range is not one-to-one. Point c in the domain maps to three points in the range. Points v, y, and z in the

range are each mapped from two points in the domain. You can imagine that in the upper van, one person

is sending messages to three different people in the lower van. In the lower van, three people are receiving

messages from two different senders. “Dupes” like this are okay in a general mapping. In some situations,

“dupes” are not allowed, as you’ll see later in this chapter.

Here’s a challenge!

Examine Fig. 13-2. Suppose the upper rectangle represents the set of all positive real numbers, and the

lower rectangle represents the set of all negative real numbers. Also imagine that the upper oval represents

Positive reals

Positive

rationals

Negative

rationals

Negative reals

Mapping:

Multiply by –1

Figure 13-2 A mapping from the positive rational

numbers to the negative rational numbers.