Definition:Finite Discontinuity

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 finite discontinuity of $f$ either:
 * $(1): \quad a$ is a removable discontinuity

or:
 * $(2): \quad a$ is a jump discontinuity.