Definition:Domain (Relation Theory)/Relation/Class Theory
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Definition
Let $V$ be a basic universe.
Let $\RR \subseteq V \times V$ be a relation in $V$.
The domain of $\RR$ is defined and denoted as:
- $\Dom \RR := \set {x \in V: \exists y \in V: \tuple {x, y} \in \RR}$
That is, it is the class of all $x$ such that $\tuple {x, y} \in \RR$ for at least one $y$.
Also known as
Some sources refer to the domain of $\RR$ as the domain of definition of $\RR$.
Some sources use a distinctive typeface, for example, $\map {\mathsf {Dom} } \RR$.
Also see
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 8$ Relations