\begin{definition}[Definition:Convergent Mapping/Real Function]
Let $f: \R \to \R$ be a real function defined everywhere on $A_1$ ''except possibly'' at $c$.
Let $\map f x$ tend to the limit $L$ as $x$ tends to $c$.
Then $f$ '''converges to the limit $L$ as $x$ tends to $c$'''.
\end{definition}