Definition:Continuous Real Function/Point

Definition
Let $A \subseteq \R$ be any subset of the real numbers, and $f: A \to \R$ be a function.

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

We say that $f$ is continuous at $x$ when the limit of $f \left({y}\right)$ as $y \to x$ exists and:
 * $\displaystyle \lim_{y \to x} \ f \left({y}\right) = f \left({x}\right)$