Editing Step function (section)

{{Short description|Linear combination of indicator functions of real intervals}}
{{About|a piecewise constant function|the unit step function|Heaviside step function}}

In mathematics, a [[function (mathematics)|function]] on the [[real number]]s is called a '''step function''' if it can be written as a [[finite set|finite]] [[linear combination]] of [[indicator function]]s of [[interval (mathematics)|interval]]s. Informally speaking, a step function is a [[piecewise]] [[constant function]] having only finitely many pieces.
[[Image:StepFunctionExample.png|thumb|right|250px|An example of step functions (the red graph). In this function, each constant subfunction with a function value ''α<sub>i</sub>'' (''i'' = 0, 1, 2, ...) is defined by an interval ''A<sub>i</sub>'' and intervals are distinguished by points ''x<sub>j</sub>'' (''j'' = 1, 2, ...). This particular step function is [[Continuous function#Directional and semi-continuity|right-continuous]].]]