Definition:Discontinuity (Real Analysis)/Removable/Definition 2

Definition
Let $X \subseteq \R$ be a subset of the real numbers.

Let $f: X \to \R$ be a real function.

Let $f$ be discontinuous at $c \in X$.

The point $c$ is a removable discontinuity of $f$ there exists $b \in \R$ such that the function $f_b$ defined by:
 * $\map {f_b} x = \begin {cases} \map f x &: x \ne c \\ b &: x = c \end {cases}$

is continuous at $c$.

Also see

 * Equivalence of Definitions of Removable Discontinuity of Real Function