ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11440 on D180: Quotient set
F11440
Formulation 2
Let $X$ be a D11: Set such that
(i) ${\sim} \subseteq X \times X$ is an D178: Equivalence relation on $X$
(ii) \begin{equation} \forall \, x \in X : [x]_{\sim} : = \{ y : (x, y) \in {\sim} \} \end{equation}
The quotient set of $X$ modulo ${\sim}$ is the D11: Set \begin{equation} X / {\sim} : = \{ [x]_{\sim} : x \in X \} \end{equation}