Continuity-Piecewise Constant Function
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10-5-2018
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Continuity-Piecewise Constant Function
A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The Heaviside step function, rectangle function, and square wave are examples of one-dimensional piecewise constant functions. Examples in two dimensions include 
and ![R[|_z_|]](http://mathworld.wolfram.com/images/equations/PiecewiseConstantFunction/Inline2.gif)
(illustrated above) for 
a complex number, ![R[z]](http://mathworld.wolfram.com/images/equations/PiecewiseConstantFunction/Inline4.gif)
the real part, and 
the floor function. The nearest integer function is also piecewise constant.
Weisstein, Eric W. "Piecewise Constant Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PiecewiseConstantFunction.html
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