\begin{definition}[Definition:Continuous Real Function at Point/Definition 2]
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 $A$.
'''$f$ is continuous at $x$''' {{iff}} the limit $\ds \lim_{y \mathop \to x} \map f y$ exists and:
:$\ds \lim_{y \mathop \to x} \map f y = \map f {\lim_{y \mathop \to x} y}$
\end{definition}