Addition

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This editable Main Article is under development and subject to a disclaimer.

[edit intro]

## Contents

* 1 Properties
* 1.1 Commutativity
* 1.2 Associativity
* 1.3 Zero and one
* 2 Sum
* 3 Addition of natural and real numbers
* 4 Natural numbers
* 5 Integers
* 6 Rational numbers (fractions)
* 7 Real numbers
* 8 Footnotes

Addition is the binary mathematical operation of putting numbers or quantities together (adding). The plus sign "+" means that objects are added up. The numbers that being added are called "addends" and the result is called "sum".

## Properties[edit]

### Commutativity[edit]

Addition is commutative, meaning a + b = b + a.

### Associativity[edit]

Addition is associative, meaning a + (b + c) = (a + b) + c

### Zero and one[edit]

Adding 0 to a number is not changing the number: a + 0 = 0 + a = a. For any integer a, (a + 1) means least integer greater than a, also known as successor of a.

## Sum[edit]

If S is a finite set of numbers, then all its elements can be added together using sigma notation. ∑x∈Sx

## Addition of natural and real numbers[edit]

## Natural numbers[edit]

## Integers[edit]

## Rational numbers (fractions)[edit]

Two fractions can be added up using this formula: ab+cd=ad+bcbd. However it is easier to use least common denominator.

## Real numbers[edit]

## Footnotes[edit]