Equivalence class representative ($x\in [x{]}_R$)

An equivalence class representative is any set element belonging to that equivalence class. In the finite modulo-three example, either $0$, $3$ or $6$ represents $\{0,3,6\}$. Changing the equivalence class representative changes its name but preserves the equivalence class itself. Choosing $0,1,2$ gives one representative of an equivalence class from each class; the quotient set consists of the three whole sets.