Game Development Reference
In-Depth Information
3
g. 16 8 þ 5½4 þ 3ð2 4Þ
h. 5s 9 þ 2ð4s þ 5Þ
i. 98 32 98 32
j.
ð8 2 3Þ9
More on Sets
In Chapter 3, you investigated some of the activities that involve sets. To extend
the previously developed notions, consider that when you define a set, you can
define it so that its elements bear relationships with each other. If you investigate
a set that consists of numbers that are less than 10 and greater than zero, for
example, then you can create a definition along the following lines:
fa j a
<
10
^ a j a
>
0
g
This expression reads along the lines of ''
a
such that
a
is less than 10
and a
such
that
a
is greater than 0.'' While the numbers 0 and 10 are not part of the set, all the
numbers in the set are defined by two common features: They must be greater
than 0
and
they must be less than 10. As Figure 4.2 illustrates, the features of the
numbers are based on relations.
As shown in Figure 4.2, you can illustrate the numbers greater than 0 and less
than 10 just by listing them within curly braces:
f
1, 2, 3, 4, 5, 6, 7, 8, 9
g
Figure 4.2
A set can be characterized by a set of numbers possessing common relations with numbers outside the set.
