Difference between revisions of "Addition"
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* <math>a+(-b)=a-b</math> (See also [[Subtraction]]) | * <math>a+(-b)=a-b</math> (See also [[Subtraction]]) | ||
− | == See also == | + | ==See also== |
− | * [[Arithmetic]] | + | *[[Arithmetic]] |
− | * [[Number theory]] | + | *[[Number theory]] |
− | * [[Subtraction]] | + | *[[Subtraction]] |
− | * [[ | + | *[[Hyperoperation]] |
− | + | *[[Counting]] | |
− | * [[Counting]] | ||
{{stub}} | {{stub}} | ||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Operation]] | [[Category:Operation]] |
Revision as of 18:25, 1 January 2025
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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