Definition:Discontinuity (Real Analysis)/Jump

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 $f$ :
 * $\ds \lim_{x \mathop \to c^-} \map f x$ and $\ds \lim_{x \mathop \to c^+} \map f x$ exist and are not equal

where $\ds \lim_{x \mathop \to c^-} \map f x$ and $\ds \lim_{x \mathop \to c^+} \map f x$ denote the limit from the left and limit from the right at $c$ respectively.

Note that $\map f c$ may equal either of these limits, or neither, or may not even be defined.

Also see

 * Jump Rule


 * Definition:Removable Discontinuity of Real Function
 * Definition:Discontinuity of the First Kind