# A step function, $u(t)=1$, for $t \gt 0$. What is the value of $u(0)$?

What is the value of $u(t)$ for $t=0$?

we know,

$u(t)=1$, for $t \gt 0$

$u(t)=0$, for $t \lt 0$

• Many of these questions are a better fit for mathematics.SE as they are pure math. We have kept many here and answer, but things like this are a pure mathematical convention. This definition of the step function is clearly poor, it should define the value at 1, there is no way for you to know without someone telling you what they expect to be correct. '1' is the standard EE answer. Feb 24 '13 at 7:50

It's all a matter of convention.

In mathematics they often define $u(0) = \frac{1}{2}$, which is called the half-maximum convention:

If you only want values of 0 and 1 (and not the $\frac{1}{2}$) then they usually define $u(0) = 1$, which is called the discrete form:

$u(t)=\begin{cases} 0, & n < 0, \\ 1, & n \ge 0 \end{cases}$