Definition:Discontinuity (Real Analysis)/Jump/Jump

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

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

Let $f$ be discontinuous at some point $c \in X$ such that $c$ is a jump discontinuity of $f$.

The jump at $c$ is defined as:

$\ds \lim_{x \mathop \to c^+} \map f x - \lim_{x \mathop \to c^-} \map f x$

Also known as

A jump is also known as a saltus.

Linguistic Note

The word saltus, that can occasionally be seen to mean jump, is taken from the Latin.

It means, literally, jump.