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:

$g \paren 0 = \dfrac 1 0$

$\blacksquare$

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $4$: Mappings: Exercise $1 \ \text {(ii)}$