Difference between revisions of "Addition"

Latest revision as of 19:34, 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 $3+2=5$ .

Notation

The sum of two numbers $a$ and $b$ is denoted $a+b$ , which is read "a plus b." The two numbers being added together, or $a$ and $b$ , are called addends. The sum of $f(a), f(a+1), f(a+2), f(a+3), \cdots, f(b)$ , where $f$ is a function, is denoted $\sum_{i=a}^bf(i)$ . (See also Sigma notation)

Properties

Commutativity: The sum $a+b$ is equivalent to $b+a$ .
Associativity: The sum $(a+b)+c$ is equivalent to $a+(b+c)$ . This sum is usually denoted $a+b+c$ .
Distributivity: $a(b+c)=ab+ac$
Closure: If $a$ and $b$ are both elements of $\mathbb{R}$ , then $a+b$ is an element of $\mathbb{R}$ . This is also the case with $\mathbb{N}$ , $\mathbb{Z}$ , and $\mathbb{C}$ .
Identity: $a+0=a$ for any complex number $a$ .
Inverse: The sum of a number and its additive inverse, $a+(-a)$ , is equal to zero.
Equality: If $a=b$ , then $a+c=b+c$ .
If $a$ is real and $b$ is positive, $a+b>a$ .
The sum of a number and its Complex conjugate is a real number.
$a+(-b)=a-b$ (See also Subtraction)

@@ Line 1: / Line 1: @@
-'''Addition''' is the mathematical [[operation]] which combines two quantities.  The plus sign, +, is used to indicate addition.
+'''Addition''' is the mathematical [[operation]] (it is represented by the <math>+</math> sign) which combines two quantities. The result of addition is called [[sum|a sum]]. For example, the sum of 3 and 2 is 5 because <math>3+2=5</math>.
+== 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==
+* 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>.
+* 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>.
+* 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]].
+* 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>.
+* The sum of a number and its [[Complex conjugate]] is a real number.
+* <math>a+(-b)=a-b</math> (See also [[Subtraction]])
 == See also ==
-* [[Counting]]
+* [[Arithmetic]]
-* [[Division]]
-* [[Multiplication]]
 * [[Number theory]]
 * [[Subtraction]]
+* [[Multiplication]]
+* [[Division]]
+* [[Counting]]
+{{stub}}
-{{stub}}
+[[Category:Definition]]
+[[Category:Operation]]

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Difference between revisions of "Addition"

Latest revision as of 19:34, 4 July 2019

Notation

Properties

See also