An [[Equivalence Class]] $E$ is a [[Subset|subset]] of some [[Set|set]] $X$ equipped with an [[Equivalence Relation]] $R$ (also denoted as $\sim$) such that all elements in $E$ are equivalent to one another. The notation for describing the equivalence class of a object $x\in X$ is $[x]_{R}$ (or $[x]$ if the relation is understood).
$\huge \begin{align}
\let a & \in X\\
[a]_{R} &\subseteq X \\
[a]_{R}&=\setbuild{x \in X}{a \sim x}
\end{align} $
In $R / X$, the [[Set|set]] of all [[Equivalence Class|Equivalence Classes]] ([[Quotient Set]]) contains [[Disjoint Set|disjointed sets]] whose [[Union|union]] forms $X$.