Working with Equivalence Classes and Quotient Sets

Usually when you talk about an equivalence class in a quotient set, you refer to it by using a representative, i.e. an element of that class. For example, consider $\Bbb Z/n\Bbb Z$, the integers modulo $n$. This is defined as a set of sets, but usually you just identify it with $\{0,\dotsc,n-1\}$.