# Addition

**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

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