Difference between revisions of "Absolute value"
(fixed logic error, though the language sounds a little odd.) |
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| + | <div style="border: 1px solid #c0b8cc; background-color: #f0e5ff; width: 80%; margin: 0 auto 1em auto; padding: .2em; text-align:center">This article or section needs to be rewritten, because:<BR> ''the initial statement of logic is unclear''. ([[talk:{{PAGENAMEE}}|Discuss]])</div><includeonly>[[category:Articles needing a rewrite]]</includeonly> | ||
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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>. | ||
| − | + | <!--:If <math>x</math> is a negative number, then <math>|-x| = x</math>. --> | |
| − | :If <math>x</math> is a negative number, then <math>|-x| = x</math>. | + | |
| − | + | ||
:If <math>x=0</math> then <math>|x| = 0</math>. | :If <math>x=0</math> then <math>|x| = 0</math>. | ||
Revision as of 01:40, April 15, 2016
the initial statement of logic is unclear. (Discuss)
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
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 (sometimes called the modulus). 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.
