Jump Discontinuity/Examples/Example 2
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Example of Jump Discontinuity
Let $f: \R \to \R$ be the real function defined as:
- $\forall x \in \R: \map f x = \begin {cases} 0 & : x > 1 \\ 1 & : x < 1 \\ \dfrac 1 2 & : x = 1 \end {cases}$
Then $f$ has a jump discontinuity at $x = 1$.
In this case, $\map f 1$ is defined, but equals neither limit.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): discontinuity
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): discontinuity