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Equivalence relation : ウィキペディア英語版
Equivalence relation

In mathematics, an equivalence relation is the relation that holds between two elements if and only if they are members of the same cell within a set that has been partitioned into cells such that every element of the set is a member of one and only one cell of the partition. The intersection of any two different cells is empty; the union of all the cells equals the original set. These cells are formally called equivalence classes.
== Notation ==
Although various notations are used throughout the literature to denote that two elements ''a'' and ''b'' of a set are equivalent with respect to an equivalence relation ''R'', the most common are "''a'' ~ ''b''" and "''a'' ≡ ''b''", which are used when ''R'' is the obvious relation being referenced, and variations of "''a'' ~''R'' ''b''", "''a'' ≡''R'' ''b''", or "''aRb''" otherwise.

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