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ALGEBRAIC DEFINITION OF ABSOLUTE VALUE
Click here for a brief discussion of the algebraic definition of absolute value
Algebraic Definition of Absolute Value
|
x
|
=
{
x ,
if x≥0
x ,
if x<0
|
That is, the absolute value of a number is itself, if the number is nonnegative.
The absolute value of a number is its opposite, if the number is negative.
The absolute value makes a useful appearance in the following formula:
For all real numbers x ,
x
2=|
x| .
|
That is, the square root of x2
is the nonnegative number which, when squared, gives x2 .
Note that
(-5)
2
=25=
5 , NOT -5 !
EXAMPLES:
Let x = 3 . Then, |x| = x .
Let x = -3 . Then, |x| = -x .