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 whole of natural theology ... resolves itself into one simple, though somewhat ambiguous proposition, That the cause or causes of order in the universe probably bear some remote analogy to human intelligence.”
—David Hume (1711–1776)
“The division between the useful arts and the fine arts must not be understood in too absolute a manner. In the humblest work of the craftsmen, if art is there, there is a concern for beauty, through a kind of indirect repercussion that the requirements of the creativity of the spirit exercise upon the production of an object to serve human needs.”
—Jacques Maritain (1882–1973)