Difference between revisions of "Addition"
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* [[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>. | ||
− | * Inverse: The sum of a number and its [[additive inverse]], <math>a+(-a)</math>, is equal to [[zero]]. | + | * Inverse: The sum of a number and its [[additive inverse]], <math>a+(-a)</math>, is equal to [[Zero (constant)|zero]]. |
* If <math>a</math> is real and <math>b</math> is positive, <math>a+b>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. | * The sum of a number and its [[Complex conjugate]] is a real number. |
Revision as of 13:47, 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
.
- Inverse: The sum of a number and its additive inverse,
, is equal to zero.
- 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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