Category:Quotient Sets

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This category contains results about Quotient Sets.


Let $\mathcal R$ be an equivalence relation on a set $S$.

For any $x \in S$, let $\eqclass x {\mathcal R}$ be the $\mathcal R$-equivalence class of $x$.


The quotient set of $S$ induced by $\mathcal R$ is the set $S / \mathcal R$ of $\mathcal R$-classes of $\mathcal R$:

$S / \mathcal R := \set {\eqclass x {\mathcal R}: x \in S}$