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[[Image:Dirac distribution CDF.svg|325px|thumb|The Heaviside step function, using the half-maximum convention]]
The '''Heaviside step function''', or the '''unit step function''', usually denoted by {{mvar|H}} or {{mvar|θ}} (but sometimes {{mvar|u}}, {{math|'''1'''}} or {{math|{{not a typo|𝟙}}}}), is a [[step function]], named after [[Oliver Heaviside]] (1850–1925), the value of which is [[0 (number)|zero]] for negative arguments and [[1 (number)|one]] for positive arguments. It is an example of the general class of [[step function]]s, all of which can be represented as [[Linear combination|linear combinations]] of translations of this one.
The function was originally developed in [[operational calculus]] for the solution of [[differential equation]]s, where it represents a signal that switches on at a specified time and stays switched on indefinitely. [[Oliver Heaviside]], who developed the operational calculus as a tool in the analysis of telegraphic communications, represented the function as {{math|'''1'''}}.
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