\begin{definition}[Definition:Finite Discontinuity]
Let $A \subseteq \R$ be a subset of the real numbers.
Let $f: A \to \R$ be a real function.
Let $f$ be discontinuous at $a \in A$.
The point $a$ is a '''finite discontinuity''' of $f$ {{iff}} either:
:$(1): \quad a$ is a removable discontinuity
or:
:$(2): \quad a$ is a jump discontinuity.
Category:Definitions/Continuity
\end{definition}