Definition:Discontinuity of the First Kind/Definition 2

Definition
Let $X$ be an open subset of $\R$.

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

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

$c$ is known as a discontinuity of the first kind of $f$ either:
 * $c$ is a jump discontinuity

or:
 * $c$ is a removable discontinuity.

Also see

 * Equivalence of Definitions of Discontinuity of the First Kind