\begin{definition}[Definition:Refinement of Finite Subdivision]
Let $\closedint a b$ be a closed interval.
Let $P, Q$ be finite subdivisions of $\closedint a b$. 
We say that $Q$ is a '''refinement''' of $P$, or that $Q$ is '''finer''' than $P$ {{iff}}: 
:$P$ is a subset of $Q$.
\end{definition}