Removable Discontinuity/Examples/Example 2
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Example of Removable Discontinuity
Let $f: \R \to \R$ be the real function defined as:
- $\forall x \in \R: \map f x = \begin {cases} x \map \sin {\dfrac 1 x} & : x \ne 0 \\ 1 & : x = 0 \end {cases}$
Then $f$ has a removable discontinuity at $x = 0$.
In this case the removable discontinuity may be removed by redefining $\map f 0$ to equal $0$.
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