Signum function: Difference between revisions
New page: The signum function, denoted <math>\text{sgn}(x)</math>, is equal to <cmath>\begin{cases} 1 & \text{for } x > 0,\\ -1 & \text{for } x < 0, \\ 0 & \text{for } x=0.\end{cases}</cmath> |
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The signum function, denoted <math>\text{sgn}(x)</math>, is equal to <cmath>\begin{cases} 1 & \text{for } x > 0,\\ | The signum function, denoted <math>\text{sgn}(x)</math>, is equal to <cmath>\begin{cases} 1 & \text{for } x > 0,\\ | ||
-1 & \text{for } x < 0, \\ 0 & \text{for } x=0.\end{cases}</cmath> | -1 & \text{for } x < 0, \\ 0 & \text{for } x=0.\end{cases}</cmath> | ||
== Properties == | |||
* The signum function is odd. | |||
* <math>\text{sgn}(x)</math> is equal to <math>\frac{|x|}{x}</math> for <math>x \neq 0</math>. | |||
Revision as of 20:28, 20 September 2008
The signum function, denoted 
, is equal to ![\[\begin{cases} 1 & \text{for } x > 0,\\ -1 & \text{for } x < 0, \\ 0 & \text{for } x=0.\end{cases}\]](http://latex.artofproblemsolving.com/4/c/9/4c9c26ce36b5f12f0ba41f4f24d9b03bfe67cf9c.png)
Properties
- The signum function is odd.
is equal to 
for 
.
for 
.
