Definition:Limit of Mapping

Real and Complex Numbers
As:
 * The real number line $\R$ under the usual metric forms a metric space;
 * The complex plane $\C$ under the usual metric forms a metric space;

the definition holds for sequences in $\R$ and $\C$.

However, see the definition of the limit of a real function below:

Limit of Real Function
The concept of the limit of a real function has been around for a lot longer than that on a general metric space.

The definition for the function on a metric space is a generalization of that for a real function, but the latter has an extra subtlety which is not encountered in the general metric space, namely: the "direction" from which the limit is approached.

Also see

 * Limit of Sequence
 * Continuity