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VC DEPARTMENT OF MATHEMATICS
REVISED SUMMER 2006
BASIC ALGEBRA REVIEW
Assume that letters such as
a
,
b
,
x
,
y
represent real numbers, unless otherwise specified.
I.
Subsets of the real numbers: Integers include whole numbers and their negatives. The rationals include all
integers AND all fractions, and have repeating decimals. Irrationals (e.g.,
π
,
2 ,
etc
.) include all other
real numbers and have nonrepeating decimals. A real number is either rational or irrational but not both.
II.
Order:
a
b
<
means that
a
is located to the left of
b
on the real number line;
a
b
≤
means that either
a
is to
the left of
b
, or
a
and
b
coincide. 0 is greater than all negative numbers, and less than all positive numbers.
III.
Absolute value:
a
b

is the distance (on number line) from
a
to
b
, disregarding direction (so the result of
an absolute value is
always
nonnegative). If
a
b
>
, then
a
b
a
b

=

; else
( )
a
b
a
b
b
a

= 

= 
. If
0
b
=
, then
0
a
a

=
is the distance from 0 to
a
. Watch negative signs closely;
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This note was uploaded on 01/17/2012 for the course MATH V04 taught by Professor Michaelbowen during the Spring '12 term at Ventura College.
 Spring '12
 MichaelBowen
 Algebra, Real Numbers, Fractions, Integers, Sets

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