Analogy With Division
This operation can be thought of (very informally) as the act of dividing the input set by the equivalence relation, hence both the name "quotient", and the notation, which are both reminiscent of division. One way in which the quotient set resembles division is that if X is finite and the equivalence classes are all equinumerous, then the number of equivalence classes in X/~ can be calculated by dividing the number of elements in X by the number of elements in each equivalence class. The quotient set X/~ may be thought of as the set X with all the equivalent points identified.
Read more about this topic: Equivalence Class
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