Category:Equivalence Classes

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This category contains results about Equivalence Classes.


Let $S$ be a set.

Let $\mathcal R \subseteq S \times S$ be an equivalence relation on $S$.

Let $x \in S$.


Then the equivalence class of $x$ under $\mathcal R$ is the set:

$\eqclass x {\mathcal R} = \set {y \in S: \tuple {x, y} \in \mathcal R}$