Definition:Symmetric Relation/Class Theory
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Definition
Let $V$ be a basic universe.
Let $\RR \subseteq V \times V$ be a relation in $V$.
$\RR$ is symmetric if and only if:
- $\tuple {x, y} \in \RR \implies \tuple {y, x} \in \RR$
Also see
- Results about symmetric relations can be found here.
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