\begin{definition}[Definition:Removable Discontinuity of Real Function/Definition 1]
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 '''removable discontinuity''' of $f$ {{iff}} the limit $\ds \lim_{x \mathop \to a} \map f x$ exists.
\end{definition}