Value of a function at Jump Discontinuitiy?

Question

How do you define value of unit step function $t=0$?

We know, $ u(t) = 0, t <0\\ $ and $ 1, t>0$ but what should be the value of $u(0)$? I find both $u(0) = 0.5$ and $u(0) = 1$ are used in different places. But I would like to know how $u(0) = 0.5.$

Answer 1

There are so many ways to define Heaviside step function. Sometimes one takes $u(0) = 0.5$ to make the graph rotational symmetric. The definition one uses depends on what one needs. See Heaviside step function on Wikipedia for more information.