quotient setとは 意味・読み方・使い方

名詞

quotient set (plural quotient sets)

1. (mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes

   Given the set of integers ${\displaystyle \mathbb {Z} }$, and the equivalence relation ${\displaystyle a\sim b\iff a\equiv b(\mod 2)\iff (a-b)\%2=0}$, the quotient set is written ${\displaystyle \mathbb {Z} /\sim =\{{\bar {0}},{\bar {1}}\}}$, consisting of the even and the odd integers.