Definition:Discontinuity (Real Analysis)/Removable/Definition 1

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 $f$ the limit $\ds \lim_{x \mathop \to c} \map f x$ exists.

Also see

 * Equivalence of Definitions of Removable Discontinuity of Real Function