• associativity: a + (b + c) = (a + b) + c, where c is also an element of the set,
• commutativity: a + b = b + a

Note 1 to entry: An addition is defined for natural numbers and extended to other classes of numbers and to mathematical entities such as vectors and matrices, and also to quantities of the same kind. An addition may be defined even for a finite set, for example the set of two elements 0 and 1 with addition modulo 2, i.e. 1 + 1 = 0.

Note 2 to entry: The addition of entities a and b is expressed by the words "a plus b". The symbol Σ is used to denote successive additions, for example $a_2+a_3+\dots +a_7$ is denoted by ${\displaystyle \sum _{i=2}^7{a}_i}$.