Definition:Continuous Real Function at Point/Definition 1

Definition

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

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

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

$f$ is continuous at $x$ if and only if the limit $\ds \lim_{y \mathop \to x} \map f y$ exists and:

$\ds \lim_{y \mathop \to x} \map f y = \map f x$