Difference between revisions of "Addition"
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== Notation == | == Notation == | ||
− | The sum of two numbers <math>a</math> and <math>b</math> is denoted <math>a+b</math>, which is read "a plus b." The sum of <math>f(a), f(a+1), f(a+2), f(a+3), \cdots, f(b)</math>, where <math>f</math> is a [[function]], is denoted <math>\sum_{i=a}^bf(i)</math>. (See also [[Sigma notation]]) | + | The sum of two numbers <math>a</math> and <math>b</math> is denoted <math>a+b</math>, which is read "a plus b." The two numbers being added together, or <math>a</math> and <math>b</math>, are called addends. The sum of <math>f(a), f(a+1), f(a+2), f(a+3), \cdots, f(b)</math>, where <math>f</math> is a [[function]], is denoted <math>\sum_{i=a}^bf(i)</math>. (See also [[Sigma notation]]) |
==Properties== | ==Properties== |
Revision as of 21:34, 23 February 2016
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
.
- 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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