Game Development Reference
In-Depth Information
Figure 4.7
If you examine the pairs in a Cartesian product, you can discern subsets.
Figure 4.8
The domain is the set of the first elements, the range is the set of the second elements.
this case represents the exploration of the way the elements of the two sets relate
to each other. The result of the exploration is called the product of the two sets.
When you proceed in this manner, you begin with a specific pattern of creating a
correspondence—or product. At the same time, after you have created the
Cartesian product, you can continue on to discover certain subsets. For example,
consider the subset of all ordered pairs that contain 1 as a first element. On the
other hand, as Figure 4.7 illustrates, you might also describe a subset that consists
of the pairs with
y
as a second element.
Domain and Range
When you generate a set of ordered pairs, the set of all elements occurring first in
the pairs is the
domain
of the relation. The set of all elements occurring second is
the
range
of the relation. With respect to the subset of ordered pairs Figure 4.8
