> [!NOTE] Definition (Quotient map) > Suppose that $E$ is an [[Equivalence relations|equivalence relation]] on a set $X$. The function $\begin{align} q_{E}:&X\to X/E \\ & x \mapsto [x]_{E} \end{align}$ is called the *quotient map* given by $E$ where $X/E$ is the [[Equivalence relations|quotient set]] of $X$ by $E.$