Definition:Subinterval of Subdivision

Definition
Let $\set {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ be a finite subdivision of $\closedint a b$.

Then for $i \in \N : i < n$ a closed interval $\closedint {x_i} {x_{i + 1} }$ is called a subinterval of the subdivision of $\closedint a b$.