Editing Sign function (section)

==Definition==
The signum function of a real number <math>x</math> is a [[piecewise]] function which is defined as follows:<ref name=":0" />
<math display="block"> \sgn x :=\begin{cases} 
-1 & \text{if } x < 0, \\
0 & \text{if } x = 0, \\
1 & \text{if } x > 0. \end{cases}</math>

The [[law of trichotomy]] states that every real number must be positive, negative or zero.
The signum function denotes which unique category a number falls into by mapping it to one of the values {{math|&minus;1}}, {{math|+1}} or {{math|0,}} which can then be used in mathematical expressions or further calculations.

For example:
<math display="block">\begin{array}{lcr}
\sgn(2) &=& +1\,, \\
\sgn(\pi) &=& +1\,, \\
\sgn(-8) &=& -1\,, \\
\sgn(-\frac{1}{2}) &=& -1\,, \\
\sgn(0) &=& 0\,.
\end{array}</math>