This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Piecewise Functions

Boole[expr]give 1 if expr is True, and 0 if it is False

Turning conditions into numbers.

Boole[expr] is a basic function that turns True and False into and . It is sometimes known as the characteristic function or indicator function.
This gives the area of a unit disk.
Click for copyable input
give the first for which is True
Piecewise[{{val1,cond1},...},val]give val if all are False

Piecewise functions.

It is often convenient to have functions with different forms in different regions. You can do this using Piecewise.
This plots a piecewise function.
Click for copyable input
Piecewise functions appear in systems where there is discrete switching between different domains. They are also at the core of many computational methods, including splines and finite elements. Special cases include such functions as Abs, UnitStep, Clip, Sign, Floor, and Max. Mathematica handles piecewise functions in both symbolic and numerical situations.
This generates a square wave.
Click for copyable input
Here is the integral of the square wave.
Click for copyable input