Definition:Convergent Mapping/Real Function

Definition
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 $c$.

Also see

 * Definition:Divergent Function