Difference between revisions of "Addition"
m (Fixed "zero" leading to disambiguation page) |
(→Properties) |
||
Line 10: | Line 10: | ||
* 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 (constant)|zero]]. | * Inverse: The sum of a number and its [[additive inverse]], <math>a+(-a)</math>, is equal to [[Zero (constant)|zero]]. | ||
+ | * Equality: If <math>a=b</math>, then <math>a+c=b+c</math>. | ||
* 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 13:48, 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.
- 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.