Definition:Continuous Real Function/Subset

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 $A$ iff $f$ is continuous at every point of $A$.

Continuity on a Singleton
The set $A$ can be any set, but there is a case in which the definition is trivial: