Definition:Field of Relation/Class Theory
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This page is about Field of Relation. For other uses, see Field.
Definition
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.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering