# 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*.

- [MLA] “binary operation.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 19 Mar 2013. Web. 19 Mar 2013. <http://platonicrealms.com/> - [APA] binary operation (19 Mar 2013). Retrieved 19 Mar 2013 from the
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