Mapping/Mistakes/Image Element Undefined

Example of Mistake in Definition of Mapping
This example of an attempted definition of a mapping contains a mistake.
 * $g: \R \to \R$ defined as: $\forall x \in \R: x \mapsto \dfrac 1 x$

Explanation
The image of the element $0 \in \R$ is undefined:
 * $g \paren 0 = \dfrac 1 0$