A binary operation under which each pair of elements, called the terms of the addition, is made to correspond to a new element called the sum of these terms.

We can define an addition operation in different sets such as sets of numbers, sets of relations, sets of geometric shapes, etc.

The inverse operation of addition is subtraction.

### Notation

The symbol of addition is “+” which is read as “plus”.

### Properties

- Addition is a commutative operation.

Example : 58 + 55 = 55 + 58 - Addition is an associative operation.

Example : (58 + 55) + 45 = 58 + (55 + 45) - Addition has an identity element.

Example : 58 + 0 = 0 + 58 = 58

### Example

Addition of whole numbers : 58 + 55 = 113

The numbers 58 and 55 are the addends of addition.

The number 113 is the sum.

\(\)\begin{matrix}58 & + & 55 & = & 113\\ \textrm{Addend}&|&\textrm{Addend}&|&\textrm{Sum}\\ \space &\textrm{Plus}&\space&\textrm{Is equal to} & \space \end{matrix}

### Educational Note

The symbol “+” appeared for the first time in a series of annotations by the German mathematician Johann Widmann in 1481. We found the notes of one of Widmann’s students at the University of Leipzig using this symbol in 1486. This symbol also appeared in a publication by Widmann in 1489.