¦ noun Mathematics & Logic the class of all members of a set that are in a given equivalence relation.

<*mathematics*> An equivalence class is a subset whose elements
are related to each other by an equivalence relation. The
equivalence classes of a set under some relation form a
partition of that set (i.e. any two are either equal or
disjoint and every element of the set is in some class).
(1996-05-13)

In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S into equivalence classes. These equivalence classes are constructed so that elements a and b belong to the same equivalence class if, and only if, they are equivalent.

Equivalence class

In mathematics, when the elements of some set $S$ have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set $S$ into **equivalence classes**. These equivalence classes are constructed so that elements $a$ and $b$ belong to the same **equivalence class** if, and only if, they are equivalent.

Formally, given a set $S$ and an equivalence relation $\,\sim \,$ on $S,$ the *equivalence class* of an element $a$ in $S,$ denoted by $[a],$ is the set

When the set $S$ has some structure (such as a group operation or a topology) and the equivalence relation $\,\sim \,$ is compatible with this structure, the quotient set often inherits a similar structure from its parent set. Examples include quotient spaces in linear algebra, quotient spaces in topology, quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories.

Pronunciation examples for equivalence class

1. defines an equivalence class that

2. defines an equivalence class specified entirely