# Unit step function

The unit step function $U \colon \mathbb{R} \rightarrow \left\{ 0, \dfrac{1}{2}, 1 \right\}$ is defined by $$U(t)=\left\{ \begin{array}{ll} 0 &, \quad t<0 \\ \dfrac{1}{2}&, \quad t=0 \\ 1 &, \quad t>0. \end{array} \right.$$