Game Development Reference
In-Depth Information
Table 3.1
Venn Diagram Descriptions
Item
Discussion
Diagram 1
Set A forms a union with set B. In this relationship, the two sets share
common elements, but at the same time, the resulting set consists of all
elements that the two sets contain.
Diagram 2
Set A forms an intersection with set B. The two sets contain common
elements, and the common elements constitute the intersection of the
two sets.
Diagram 3
The disjunction of the two sets, A and B, creates a situation in which you
must form an ''or'' statement to account for the elements of the two sets.
Diagram 4
Set B is a subset of set A. In this case, each element of set B is also an
element of set A.
Diagram 5
This is a compound relationship. First, you create an intersection between
sets A and B. Given this intersection, you then find the union of the
intersected elements and set C.
Diagram 6
This is a compound relationship. First, you find a union of sets A and B.
Such a union takes the form of Diagram 1. However, the second part of
the statement defining Diagram 6 calls for set C to form an intersection
with the union of A and B. The intersection then excludes elements that
are not common to A, B, and C.
Negative Numbers with Powers
When you use a negative number as an exponent, you create the inverse of the
power. Consider the following expressions:
1
a
2
1
2
2
¼
1
4
a
2
2
2
¼
¼
1
a
3
1
2
3
¼
1
8
a
3
2
3
¼
¼
1
a
4
1
2
4
¼
1
16
a
4
2
4
¼
¼
In each instance, the negative exponent signals that you are dealing with the
inverse of the number. This holds true for all numbers not equal to zero and all
exponents greater than zero. A number multiplied by its inverse equals 1.
Multiplication
If you are working with base numbers that are the same, then you can add the
exponents of the numbers to multiply the numbers. Consider the following
