Game Development Reference
In-Depth Information
represent the set of integers:
Z
¼f
0,
1,
2,
3,
4,
5...
g
As with counting numbers and whole numbers, you see the curly braces, which
represent a set. You also see a
plus-or-minus
sign preceding each of the numbers in
the set. Use of the plus-or-minus sign serves as a way to shorten the mathematical
expression from its longer form:
Z
¼f
...
5,
4,
3,
2,
1, 0,
þ
1,
þ
2,
þ
3,
þ
4,
þ
5...
g
The second expression conveys the same information as the first, but in this case, a
minus sign (
) precedes each negative number and a positive sign (+) precedes
each positive number. Likewise, you see that ellipses precede and follow the
numbers. Notice the zero possesses no sign. You can certainly apply a sign to a zero
without doing any harm, but the fact remains that the sign has no effect on zero.
Zero is neither negative nor positive.
When you use integers, you never need to indicate a positive value using a plus
sign. As a matter of common practice, if you see a number standing alone
without a sign, it is positive. Here is another way to show the longer form of the
set of integers:
Z
¼f
...
5,
4,
3,
2,
1, 0, 1, 2, 3, 4, 5 . . .
g
So far you have looked at natural numbers, whole numbers, and integers. The
relationship between these number systems is as follows: Every natural number
and every whole number is a number in the set of integers. In other words, W is a
subset of Z and N is a subset of Z. Also, recall that N is a subset of W.
Rational Numbers
Even if you can count things at hand, recognize things when they are entirely
absent, or count them in a negative or absent form, you still face situations in
which you need to account for things that are not quite whole. To deal with this
situation, one approach involves working with the concept that you can establish
a ratio between two numbers.
As Figure 2.4 illustrates, picture the situation of a potter whom customers have
asked to make five pots. The potter has made three pots. A customer arrives and
requests to know how much of the work of making the pots has been completed.
The potter can reply by asking the customer to imagine the whole set of five pots
