Jump Discontinuity/Examples/Example 1

Example of Jump Discontinuity

Let $f: \R \to \R$ be the real function defined as:

$\forall x \in \R: \map f x = \begin {cases} 1 & : x < 2 \\ 2 & : x \ge 2 \end {cases}$

Then $f$ has a jump discontinuity at $x = 2$.

In this case, $\map f 2$ is defined, and equals the limit from the right.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): jump discontinuity