Definition:Discontinuity (Real Analysis)/Jump/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 $c \in X$ 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.

Sources

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Some Important Properties of Laplace Transforms: $5$. Laplace transform of derivatives
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): jump or saltus
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): saltus: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): jump
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): jump