Difference between revisions of "Addition"
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− | '''Addition''' is the mathematical [[operation]] which combines two quantities. | + | '''Addition''' is the mathematical [[operation]] which combines two quantities. The result of addition is called [[sum|a sum]]. |
+ | |||
+ | == Notation == | ||
+ | The sum of two numbers <math>a</math> and <math>b</math> is denoted <math>a+b</math>, which is read "a plus b." The sum of <math>f(a), f(a+1), f(a+2), f(a+3), ..., f(b)</math>, where <math>f</math> is a [[function]], is denoted <math>\sum_{i=a}^bf(i)</math>. (See also [[Sigma notation]]) | ||
+ | |||
+ | ==Properties== | ||
+ | * 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>. | ||
+ | * [[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>. | ||
+ | * If <math>a</math> is real and <math>b</math> is positive, <math>a+b>a</math>. | ||
+ | * The sum of a number and its [[Complex conjugate]] is a real number. | ||
+ | * <math>a+(-b)=a-b</math> (See also [[Subtraction]]) | ||
== See also == | == See also == |
Revision as of 12:41, 8 November 2008
Addition is the mathematical operation which combines two quantities. The result of addition is called a sum.
Notation
The sum of two numbers and is denoted , which is read "a plus b." 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 .
- Closure: If and are both elements of , then is an element of . This is also the case with , , and .
- Identity: for any complex number .
- 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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