# Difference between revisions of "Addition"

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* Commutativity: The sum <math>a+b</math> is equivalent to <math>b+a</math>. | * Commutativity: The sum <math>a+b</math> is equivalent to <math>b+a</math>. | ||

* Associativity: The sum <math>(a+b)+c</math> is equivalent to <math>a+(b+c)</math>. This sum is usually denoted <math>a+b+c</math>. | * Associativity: The sum <math>(a+b)+c</math> is equivalent to <math>a+(b+c)</math>. This sum is usually denoted <math>a+b+c</math>. | ||

+ | * Distributivity: a(b+c)=ab+ac | ||

* [[Closure]]: If <math>a</math> and <math>b</math> are both elements of <math>\mathbb{R}</math>, then <math>a+b</math> is an element of <math>\mathbb{R}</math>. This is also the case with <math>\mathbb{N}</math>, <math>\mathbb{Z}</math>, and <math>\mathbb{C}</math>. | * [[Closure]]: If <math>a</math> and <math>b</math> are both elements of <math>\mathbb{R}</math>, then <math>a+b</math> is an element of <math>\mathbb{R}</math>. This is also the case with <math>\mathbb{N}</math>, <math>\mathbb{Z}</math>, and <math>\mathbb{C}</math>. | ||

* Identity: <math>a+0=a</math> for any complex number <math>a</math>. | * Identity: <math>a+0=a</math> for any complex number <math>a</math>. |

## Revision as of 12:33, 16 June 2019

**Addition** is the mathematical operation (it is represented by the sign) which combines two quantities. The result of addition is called a sum. For example, the sum of 3 and 2 is 5 because .

## Notation

The sum of two numbers and is denoted , which is read "a plus b." The two numbers being added together, or and , are called addends. The sum of , where is a function, is denoted . (See also Sigma notation)

## Properties

- Commutativity: The sum is equivalent to .
- Associativity: The sum is equivalent to . This sum is usually denoted .
- Distributivity: a(b+c)=ab+ac
- Closure: If and are both elements of , then is an element of . This is also the case with , , and .
- Identity: for any complex number .
- Inverse: The sum of a number and its additive inverse, , is equal to zero.
- Equality: If , then .
- If is real and is positive, .
- The sum of a number and its Complex conjugate is a real number.
- (See also Subtraction)

## See also

*This article is a stub. Help us out by expanding it.*