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 sqrt(z^2)/z and R[|_z_|] (illustrated above) for z a complex number, R[z] the real part, and |_x_| the floor function. The nearest integer function is also piecewise constant.

See also

Constant Function, Decreasing Function, Increasing Function, Piecewise Function, Piecewise Linear Function

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Cite this as:

Weisstein, Eric W. "Piecewise Constant Function." From MathWorld--A Wolfram Web Resource.

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