\begin{definition}[Definition:Removable Discontinuity of Real Function/Definition 2]
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}} there exists $b \in \R$ such that the function $f_b$ defined by:
:$\map {f_b} x = \begin {cases} \map f x &: x \ne a \\ b &: x = a \end {cases}$
is continuous at $a$.
\end{definition}