Definition:Discontinuity (Real Analysis)/First Kind

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 $c \in X$.

Then $c$ is called a jump discontinuity of $f$ :
 * $\displaystyle \lim_{ x \to c^{-} } f \left({ x }\right)$ and $\displaystyle \lim_{ x \to c^{+} } f \left({ x }\right)$ exist

Also known as
Jump discontinuities are also known as discontinuities of the first kind