In mathematics, an equivalence relation is, loosely, a binary relation on a set that specifies how to split up (i.e. partition) the set into subsets such that every element of the larger set is in exactly one of the subsets. Any two elements of the larger set are then considered "equivalent" with respect to the equivalence relation if and only if they are also elements of the same subset.
An equivalence relation partitions a set into several disjoint subsets, called equivalence classes. All the elements in a given equivalence class are equivalent among themselves, and no element is equivalent with any element from a different class.
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