\begin{definition}[Definition:Piecewise Continuous Function]
Let $f$ be a real function defined on a closed interval $\closedint a b$.
$f$ is '''piecewise continuous''' {{iff}}:
:there exists a finite subdivision $\set {x_0, x_1, \ldots, x_n}$ of $\closedint a b$, where $x_0 = a$ and $x_n = b$, such that:
::for all $i \in \set {1, 2, \ldots, n}$, $f$ is continuous on $\openint {x_{i − 1} } {x_i}$.
Further conditions can be placed on this definition to add specialisation as necessary:
\end{definition}