1
L1 Real Numbers; Algebra Review
Sets of Numbers
Natural numbers
:
Whole numbers
:
Integers
:
Rational numbers
:
{
a
x
x
b
=
, where
a
and
b
are integers and
}
0
b
≠
Note
:
1)
Any integer
m
can be written as
1
m
, thus, all
integers are rational numbers.
2)
Rational numbers also include repeating and
terminating decimals, for example:
1
0.333...
0.3
3
=
=
0.9
1.0
1
=
=
Irrational numbers
:
Includes any real number that is not
a rational number, for example:
Real numbers
:
The rational and irrational numbers
together.
2
Operations on the Set of Real Numbers
Addition:
a
b
+
Multiplication:
ab
Properties of Real Numbers
Commutative Properties
:
Associative Properties
:
Identity Properties
:
There is a unique number
0
, called
additive identity
,
such
that
There is a unique number
1
, called
multiplicative identity
,
such that
Inverse Properties
:
There is a unique number
b
−
,
additive inverse
or
negative of b
, such that
Subtraction
:
a
b
−
=
For
0
b
≠
, there is a unique number
1/
b
,
multiplicative
inverse
or
reciprocal of b
, such that
Division
: (
0
b
≠
)
/
a b
=

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