quotient set

== English == === Noun === quotient set (plural quotient sets) (mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes Given the set of integers Z {\displaystyle \mathbb {Z} } , and the equivalence relation a ∼ b ⟺ a ≡ b ( mod 2 ) ⟺ ( a − b ) % 2 = 0 {\displaystyle a\sim b\iff a\equiv b(\mod 2)\iff (a-b)\%2=0} , the quotient set is written Z / ∼= { 0 ¯ , 1 ¯ } {\displaystyle \mathbb {Z} /\sim =\{{\bar {0}},{\bar {1}}\}} , consisting of the even and the odd integers. ==== Translations ==== ==== See also ==== quotient topology (“a topology on a quotient set derived from a topology on the generating set”) quotient space (“a topological space constructed by endowing the quotient set with its quotient topology”)