Definition:Continuous Real Function/Point

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

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

Let $x \in A$ be a point of $A$.

Definition 2
Hence for various definitions of limits:

Also defined as
Often continuity is only defined for limit points of the domain.

Also see

 * Equivalence of Definitions of Continuous Real Function at Point


 * Definition:Discontinuous Real Function at Point