One of the basic arithmetic operations. The result of addition is called the sum. The sum of two numbers $a$ and $b$ is denoted by $a+b$, and $a$ and $b$ are called the summands. Addition of numbers is commutative: $a+b=b+a$, and associative: $(a+b)+c=a+(b+c)$. The operation inverse to addition is called subtraction.
Addition is also the name usually given to the operation in an Abelian group (in additive notation) and to the binary operation in a ring under which its elements form an Abelian group. Here also, addition is associative and commutative. Sometimes, a non-commutative operation in a group is called addition, such as in the case of a multi-operator group.
Addition. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Addition&oldid=31372