# binary operation

A binary operation is a function that maps ordered pairs of elements of a set to elements of the set. For example, addition of natural numbers maps every pair of natural numbers to their sum, so addition is a binary operation on natural numbers.

Apart from the common operations such as addition, multiplication, dot-product, etc., a binary operation is commonly denoted by placing an asterisk between the elements: $$a*b$$.

If a binary operation has the property that $$a*b=b*a$$ for every $$a$$ and $$b$$ in the set, then the operation is said to be commutative. If a binary operation has the property that $$(a*b)*c=a*(b*c)$$ for all $$a$$, $$b$$, and $$c$$ in the set, then the operation is said to be associative.