ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D4423
Relation class
Formulation 0
Let $X \neq \emptyset$ be a D11: Set.
Let $R \subseteq X \times Y$ be a D4: Binary relation.
The relation class of $x \in X$ with respect to $R$ is the D11: Set \begin{equation} R(x) : = \{ y \mid (x, y) \in R \} \end{equation}
Formulation 1
Let $B = (X \times Y, R)$ be a D4: Binary relation such that
(i) $X \neq \emptyset$
The relation class of $x \in X$ in $B$ is the D11: Set \begin{equation} R(x) : = \{ y : (x, y) \in R \} \end{equation}
Also known as
Set of related elements
Children
▶ D179: Equivalence class