Definition:Mapping/Defined
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Definition
A mapping $f \subseteq S \times T$ is defined at $x \in S$ if and only if:
- $\exists y \in T: \tuple {x, y} \in f$
If for some $x \in S$, one has:
- $\forall y \in T: \tuple {x, y} \notin f$
then $f$ is not defined or (undefined) at $x$, and indeed, $f$ is not technically a mapping at all.
Also see
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: Equivalence Relations: $\S 19$