Definition:Discontinuity (Real Analysis)/Removable

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 $a\in A$.

Also see

 * Equivalence of Definitions of Removable Discontinuity of Real Function
 * Definition:Nonremovable Discontinuity
 * Definition:Jump Discontinuity
 * Definition:Discontinuity of the First Kind