Game Development Reference
In-Depth Information
Exercise Set 2.1
To test your understanding of the systems of numbers, please identify the number set the
following numbers belong in. Identify the innermost set for each number.
Example: 4
=
2 2 N
a.
b. 2
c. 6/3
d. 5/2
e. 2/3
f. 4/5
g. 2/1
h. 1/8
i. 1/5
j.
7
p
Properties
When you work with real numbers, you do so according to a set of rules that
mathematicians often describe as
properties
. The properties of a number system
pertain to how the numbers behave when you carry out operations using them.
Figure 2.6 illustrates the basic properties of the real numbers. These properties
apply to all the number systems you have dealt with so far. However, not all
properties are applicable to all number systems. The next few sections review
these properties in detail.
Commutative Property
When you work with two numbers,
a
and
b
, the order in which you add or
multiply them is commutative. The commutative property pertains to addition
and multiplication. Consider these equations:
a þ b ¼ c
3
þ
5
¼
8
a b ¼ c
3
4
¼
12
b þ a ¼ c
5
þ
3
¼
8
b a ¼ c
4
3
¼
12
