Algebra Know-It-ALL

Are you confused?

Graphs can make relations easier to understand. In the next chapter, you’ll learn about one of the most
common graphing schemes in mathematics, and you’ll see how the above relations look when illustrated
that way.

Here’s a challenge!

Using Fig. 13-8 as a guide, define a relation that maps the set of natural numbers onto the set of rational
numbers. List the first 13 ordered pairs in this relation. Is this relation injective? Is it surjective? Is it
bijective?

Solution

Let’s represent natural numbers by the independent variable n, and corresponding rational numbers by
the dependent variable r. We can start with 0 for n, and map it into the rational number 0 for r. Then we

Examples of Relations 217

Figure 13-8 This two-dimensional list of all rationals (duplicated

from Chap. 9) suggests a way to define a relation

between the set of naturals and the set of rationals.