Definition:Field of Relation/Class Theory

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This page is about Field of Relation. For other uses, see Field.


Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation in $V$.

The field of $\RR$ is defined as:

$\Field \RR := \set {x \in V: \exists y \in V: \tuple {x, y} \in \RR} \cup \set {y \in V: \exists x \in V: \tuple {x, y} \in \RR}$

That is, it is the union of the domain of $\RR$ with its image.