Difference between revisions of "Signum function"

(New page: The signum function, denoted <math>\text{sgn}(x)</math>, is equal to <cmath>{1for x>0,1for x<0,0for x=0.</cmath>)
 
Line 1: Line 1:
 
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 $\text{sgn}(x)$, is equal to \[\begin{cases} 1 & \text{for } x > 0,\\     -1 & \text{for } x < 0, \\ 0 & \text{for } x=0.\end{cases}\]

Properties

  • The signum function is odd.
  • $\text{sgn}(x)$ is equal to $\frac{|x|}{x}$ for $x \neq 0$.