Mapping/Mistakes/Image Element Multiply Defined

Example of Mistake in Definition of Mapping

This example of an attempted definition of a mapping contains a mistake.

$h: \R \to \R$ defined as: $\forall x \in \R: x \mapsto \begin{cases} x + 1 & : x \ge 0 \\ 0 & : x \le 0 \end{cases}$

Explanation

The element $0 \in \Dom h$ is defined twice:

$h \paren 0 = 0 + 1 = 1$

and:

$h \paren 0 = 0$

$\blacksquare$

Sources

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