Definition 5.1.1 (Partition).label Let $[a,b]\suf\R$, then a partition of $[a,b]$ is a sequence

\begin{align*}P=\curl{x_j}^{n}_{j=0}=\curl{a=x_0\leq \cds\leq x_n=b}\end{align*}

The collection $\scr{P}([a,b])$ is the set all partitions of $[a,b]$