Equivalence class – TheoremDex

▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Relation class

Equivalence class

Formulation 0

Let $X$ be a D11: Set such that

(i)	\begin{equation} X \neq \emptyset \end{equation}
(ii)	${\sim} \subseteq X \times X$ is an D178: Equivalence relation on $X$

The equivalence class of $x \in X$ with respect to ${\sim}$ is the D11: Set \begin{equation} \{ y : (x, y) \in {\sim} \} \end{equation}

Child definitions

» D4430: Constancy class

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