The Heaviside step function is a discontinuous function whose value is $0$ for all negative values and $1$ for non-negative values. It is defined as

H(x) \equiv \begin{cases}0 & \text{for } x<0 \ 1 & \text{for } x > 0\end{cases}.

For analytical applications, H is usually not defined at x = 0, although for many numerical use cases, the average is often used, namely H(0) = \frac{1}{2}.

09:38 Saturday 15 May 2021