Editing Heaviside step function (section)

{{Short description|Indicator function of positive numbers}}
{{refimprove|date=December 2012}}
{{Infobox mathematical function
| name = Heaviside step
| image = Dirac distribution CDF.svg
| imagesize = 325px
| caption = The Heaviside step function, using the half-maximum convention
| general_definition = <math display="block">H(x) := \begin{cases} 1, & x \geq 0 \\ 0, & x < 0 \end{cases}</math>{{dubious|reason=This definition is not "general" because it adopts the H(0)=1 convention (hence disregarding other conventions).|date=August 2024}}
| fields_of_application = Operational calculus
}}

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]], the value of which is [[0 (number)|zero]] for negative arguments and [[1 (number)|one]] for positive arguments.  Different conventions concerning the value {{math|''H''(0)}} are in use. It is an example of the general class of step functions, all of which can be represented as [[linear combination]]s 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. Heaviside developed the operational calculus as a tool in the analysis of telegraphic communications and represented the function as {{math|'''1'''}}.