# Addition

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Addition.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Addition&oldid=31372

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article