Step Function
A function on the reals R is a step function if it can be written as a finite linear combination of semi-open intervals [a,b) subset= R. Therefore, a step function f can be written as
| f(x)=alpha_1f_1(x)+...+alpha_nf_n(x), |
where alpha_i in R, f_i(x)=1 if x in [a_i,b_i) and 0 otherwise, for i=1, ..., n.
See also
Heaviside Step FunctionExplore with Wolfram|Alpha
WolframAlpha
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Cite this as:
Weisstein, Eric W. "Step Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StepFunction.html