The Heaviside functions in the following?

Question

For $(\mu_{i})_{i=\overline{1,n}}$ are real positive parameters, we have $H$ is the Heaviside function, i.e $$\forall i = \overline{1,n}, ~~~~H(u-\mu_i)=\left\{\begin{array}{ll} 1 & \quad \mbox{if }\ u>\mu_i \\[0.1cm] 0 & \quad \mbox{if }\ u<\mu_i . \end{array} \right.$$

Please I would appreciate the feedback.

Answer 1

Suppose that $\mu_1<\mu_2<\cdots<\mu_n$. Then if $u<\mu_1$, then $S=0$. If $u\in(\mu_i,\mu_{i+1})$, then $S=i$. If $u>\mu_n$, then $S=n$.