Mapping/Mistakes

Examples of Mistakes in Definition of Mappings

Here are some supposed definitions of mappings which contain mistakes.

Image Elements not in Codomain

$f: \N \to \N$ defined as: $\forall x \in \N: x \mapsto x - 7$

Image Element Undefined

$g: \R \to \R$ defined as: $\forall x \in \R: x \mapsto \dfrac 1 x$

Image Element Multiply Defined

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

Mapping not Well-Defined

$\theta: \Q \to \Z$ defined as: $\forall m, n \in \Z, n \ne 0: \dfrac m n \mapsto m + n$