Jump Discontinuity/Examples/Example 3
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Example of Jump Discontinuity
Let $f: \R \to \R$ be the real function defined as:
- $\forall x \in \R: \map f x = \begin {cases} -1 & : x < 0 \\ 1 & : x > 0 \\ \text {undefined} & : x = 0 \end {cases}$
Then $f$ has a jump discontinuity at $x = 1$.
In this case, $\map f 0$ is not defined.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): jump discontinuity
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): jump discontinuity