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
Famous quotes containing the words analogy and/or division:
“The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
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