# Definition:Continuous Real Function/Subset

< Definition:Continuous Real Function(Redirected from Definition:Continuous Real Function on Subset)

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## Definition

Let $A \subseteq \R$ be any subset of the real numbers.

Let $f: A \to \R$ be a real function.

Then **$f$ is continuous on $A$** if and only if $f$ is continuous at every point of $A$.