Difference between revisions of "Absolute value"
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| − | The absolute value of a number is a measure of the size of that number. The absolute value of <math>x</math> is written <math>|x|</math>. | + | The '''absolute value''' of a number is a measure of the size of that number. The absolute value of <math>x</math> is written <math>|x|</math>. |
:If <math>x</math> is a positive number, then <math>|x| = x</math>. | :If <math>x</math> is a positive number, then <math>|x| = x</math>. | ||
Revision as of 22:04, March 8, 2008
The absolute value of a number is a measure of the size of that number. The absolute value of 
is written 
.
- If is a positive number, then
.
- If is a negative number, then
.
- If
then 
.
Absolute value has several useful properties. One is the multiplicative property. If and 
are two numbers, then 
. Another is the triangle inequality, which is the fact that 
. For example, if 
and 
, then 
, while 
. In this case, the triangle inequality is the fact that 2 is not more than 8.
Complex numbers also have an absolute value. If 
is a complex number with real part and imaginary part , then 
. If we represent 
as a point in the complex plane with coordinates 
, then 
is the distance from this point to the origin. The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.
