Definition:Equivalence Relation/Also denoted as

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When discussing equivalence relations, various notations are used for $\left({x, y}\right) \in \mathcal R$.

Examples are:

$x \equiv \map y {\mathcal R}$
$x \equiv y \pmod {\mathcal R}$
$x \sim y$

and so on.

Specialised equivalence relations generally have their own symbols, which can be defined as they are needed.

Such symbols include:

$\cong$, $\equiv$, $\sim$, $\simeq$, $\approx$