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: a(b+c)=ab+ac | ||
* [[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>. | ||
Revision as of 11:33, 16 June 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: 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)
.
is equivalent to 
. This sum is usually denoted 
.
, then 
, 
, and 
.
for any complex number 
, is equal to 
, then 
.
.
(See also See also
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