Definition:Discontinuity (Real Analysis)/Removable/Definition 2
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Definition
Let $X \subseteq \R$ be a subset of the real numbers.
Let $f: X \to \R$ be a real function.
Let $f$ be discontinuous at $c \in X$.
The point $c$ is a removable discontinuity of $f$ if and only if there exists $b \in \R$ such that the function $f_b$ defined by:
- $\map {f_b} x = \begin {cases} \map f x &: x \ne c \\ b &: x = c \end {cases}$
is continuous at $c$.
Also see
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