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 $\eqclass x \RR$.

The symbol used on is a modified version of an attempt to reproduce the heavily-bolded $\sqbrk x_\RR$ found in.

Other variants, with selected examples of texts which use those variants:


 * uses $\overline x$ for $\eqclass x \RR$.


 * uses $E_x$ for $\eqclass x \RR$.


 * uses $\bigsqcup_\RR \mkern {-28 mu} {\raise 1pt x} \ \ $ for $\eqclass x \RR$, which is even more challenging to render in our installed version of $\LaTeX$ than $\eqclass x \RR$ itself.


 * uses $\boldsymbol [ x \boldsymbol ]_\RR$.


 * uses $\map {p_\RR} x$.


 * uses $x / \RR$ for $\eqclass x \RR$ (compare the notation for quotient set). This source also suggests $x_\RR$ as a variant.


 * uses $\map \pi x$ for $\eqclass x \RR$.