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 ().
is an operation that applies to two quantities or expressions 
and 
.
is a map 
such that 
is defined for every pair of elements in 
, and
uniquely associates each pair of elements in 
to some element of 
.
from 
to 
include addition (
), subtraction (-), multiplication 
) and division (
).