A binary operation 
is an operation that applies to two quantities or expressions 
and 
.
A binary operation on a nonempty set 
is a map 
such that
1. 
is defined for every pair of elements in 
, and
2. 
uniquely associates each pair of elements in 
to some element of 
.
Examples of binary operation on 
from 
to 
include addition (
), subtraction (
), multiplication 
) and division (
).
A group operation is a binary operation satisfying the axioms needed to make the underlying set into a group.
