Definition:Equivalence Class/Notation

Definition
The notation used to denote an equivalence class varies throughout the literature, but is often some variant on the square bracket motif $\left[\!\left[{x}\right]\!\right]_\mathcal R$.

Other variants:


 * uses $\overline x$ for $\left[\!\left[{x}\right]\!\right]_\mathcal R$.


 * uses $\pi \left({x}\right)$ for $\left[\!\left[{x}\right]\!\right]_\mathcal R$.


 * uses $E_x$ for $\left[\!\left[{x}\right]\!\right]_\mathcal R$.


 * uses $\bigsqcup_{\mathcal R} \mkern {-28 mu} {\raise 1pt x} \ \ $ for $\left[\!\left[{x}\right]\!\right]_\mathcal R$, which is challenging to render in our installed version of $\LaTeX$.


 * uses $p_{\mathcal R} \left({x}\right)$.


 * uses $x / \mathcal R$ for $\left[\!\left[{x}\right]\!\right]_\mathcal R$ (compare the notation for quotient set).