Definition:Discontinuous Mapping/Real Function
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Definition
Let $f$ be a real function.
Then $f$ is discontinuous if and only if there exists at least one $a \in \R$ at which $f$ is discontinuous.
At a Point
Let $A \subseteq \R$ be a subset of the real numbers.
Let $f : A \to \R$ be a real function.
Let $a\in A$.
Then $f$ is discontinuous at $a$ if and only if $f$ is not continuous at $a$.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): discontinuous
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): discontinuous function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): discontinuous function
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): discontinuous function