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relation on the equivalence class of an element in is denoted or, equivalently, to emphasize its equivalence relation , and is defined as the set of all elements in with which is -related. The definition of equivalence relations implies that the equivalence classes form a partition of meaning, that every element of the set belongs to exactly one equivalence class. The set of the equivalence classes is sometimes called the quotient set or the quotient space of by and is denoted

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