Heaviside step function

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Heaviside step
The Heaviside step function, using the half-maximum convention
General information
General definition	$${\displaystyle H(x):={\begin{cases}1,&x\geq 0\\0,&x<0\end{cases}}}$$[dubious – discuss]
Fields of application	Operational calculus

The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.

The function was originally developed in operational calculus for the solution of differential equations, 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 1.