Game Development Reference
In-Depth Information
Additive Identity
When you add zero to a number, the outcome is the number itself. Zero in this
case is called the additive identity, such that:
a þ
0
¼
0
þ a ¼ a
Multiplicative Identity
When you multiply a number by 1, you get the number itself. 1 in this case is
called the multiplicative identity, such that:
a
1
¼
1
a ¼ a
Consider the following equations:
1
a ¼ a
1
a ¼a
If you multiply
a
by 1, you get
a
. If you multiply
a
by
1, you still get
a
, but the
sign
of
a
is now changed to match the
sign
of
1
.
Additive Inverse
For a given number
a
, if you add a value to
a
that is equal to and opposite in value
to
a
, then the result is zero. The number you add to
a
is called the additive
inverse, or negative, of
a
such that:
a þðaÞ¼ðaÞþa ¼
0
The additive inverse of
a
is
a
. The additive inverse of
a
is
a
.
Multiplicative Inverse
A number multiplied by its inverse is 1. The inverse of a number is the fraction
(or ratio) by which you can multiply the number to create the value of 1. For a
given number
a
, as long as
a 6¼
0, there is a number
a
, called the multiplicative
inverse, or reciprocal of
a
, such that:
a ð
1
=
aÞ¼ð
1
=
aÞa ¼
1
Consider the following equations:
4
3
¼
1
The multiplicative inverse of
a
is
a
. The multiplicative inverse of 5 is
5
.Themulti-
plicative inverse of 4000000 is
1
a
¼
1
1
5
¼
1
1
4000000
¼
1
3
4
a
;
5
;
4000000
;
1
4000000
.Thelastexampleprovesalittlemoreinvolved
