What does $\max_{i=0}^{n}$ mean?

Question

I cannot understand what exactly does this notation mean. Could someone please explain: $\max_{i=0}^{n}$. In context, I am trying to understand the expression

$$c\times \max_{i=0}^{n} h(m_i). $$

Answer 1

$\max_{i=0}^n h(m_i)$ is the greatest of the $n+1$ values $h(m_0), h(m_1), h(m_2), ..., $ and $h(m_n)$ .

So for all $i$ between $0$ and $n$, $h(m_i)\le \max_{i=0}^n h(m_i)$,

and there is $j$ between $0$ and $n$ such that $h(m_j)=\max_{i=0}^n h(m_i)$.

For example, if $h(m_i)=i$ for all $i$ between $0$ and $n$, then $\max_{i=0}^n h(m_i)=n$.