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

Definition
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 $f$ the limit $\displaystyle \lim_{x \to a}f(x)$ exists.

Also see

 * Equivalence of Definitions of Removable Discontinuity of Real Function