> [!NOTE] Definition (Refinement of Partition) > Let $[a,b]$ be a [[Closed Real Interval|closed real interval]]. Let $P,Q$ be [[Finite Partition of Closed Real Interval|finite partitions]] of $[a,b].$ Then $Q$ is a refinement of $P$ iff for all $J\in Q,$ there exists $K\in P$ such that $J \subset K.$ **Note**: Informally, the condition asserts that every endpoint in $P$ is an endpoint in $Q.$