1.Nounthe 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."