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: <math>a(b+c)=ab+ac</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>. | * [[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>. |
Latest revision as of 20:34, 4 July 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:
- 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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