Definition:Many-to-One Relation/Defined
< Definition:Many-to-One Relation(Redirected from Definition:Defined (Partial Mapping))
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Definition
Let $f \subseteq S \times T$ be a many-to-one relation.
Defined at Element
Let $s \in S$.
Then $f$ is defined at $s$ if and only if $s \in \Dom f$, the domain of $f$.
Defined on Subclass
Let $R \subseteq S$.
Then $f$ is defined on $R$ if and only if it is defined at all $r \in R$.
Equivalently, if and only if $R \subseteq \Dom f$, the domain of $f$.