Mapping/Mistakes
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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: $\forall m, n \in \Z, n \ne 0: \dfrac m n \mapsto m + n$