\begin{definition}[Definition:Equivalence Class/Notation]
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 {{ProofWiki}} is a modified version of an attempt to reproduce the heavily-bolded $\sqbrk x_\RR$ found in {{BookReference|Topology: An Introduction with Application to Topological Groups|1967|George McCarty}}.
Other variants, with selected examples of texts which use those variants:
* {{BookReference|Lectures in Abstract Algebra|1951|Nathan Jacobson|volume = I|subtitle = Basic Concepts}} uses $\overline x$ for $\eqclass x \RR$.
* {{BookReference|Sets and Groups|1965|J.A. Green}} uses $E_x$ for $\eqclass x \RR$.
* {{BookReference|Modern Algebra|1965|Seth Warner}} 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.
* {{BookReference|Elements of Abstract Algebra|1971|Allan Clark}} uses $\boldsymbol [ x \boldsymbol ]_\RR$.
* {{BookReference|A Handbook of Terms used in Algebra and Analysis|1972|A.G. Howson}} uses $\map {p_\RR} x$.
* {{BookReference|Set Theory and Abstract Algebra|1975|T.S. Blyth}} uses $x / \RR$ for $\eqclass x \RR$ (compare the notation for quotient set). This source also suggests $x_\RR$ as a variant.
* {{BookReference|Introduction to Topology|1975|Bert Mendelson|ed = 3rd|edpage = Third Edition}} uses $\map \pi x$ for $\eqclass x \RR$.
\end{definition}