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Equivalence Class

Last updated Nov 1, 2022

# Definition

Let $X$ be a Set and let $\sim$ be an Equivalence Relation

on

X

. If

\mathcal{S}

is the Partition of

X

corresponding to

\sim

(as per Correspondence of Surjective Functions, Partitions, and Equivalence Relations), then we call the elements

\mathcal{S}

the Equivalence Classes of

\sim

.

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Equivalence Class

Equivalence Class

Definition Let $X$ be a and let $\sim$ be an on $X$ . If $\mathcal{S}$ is the of $X$ corresponding to $\sim$ (as per ), then we call the elements $\mathcal{S}$ the es of $\sim$ ....

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