Difference between revisions of "Addition"

Line 1: Line 1:
'''Addition''' is the mathematical [[operation]] which combines two quantities. The plus sign, <math>+</math>, is used to indicate addition. Addition is also called [[sum|a sum]]
+
'''Addition''' is the mathematical [[operation]] which combines two quantities. The result of addition is called [[sum|a sum]].
 +
 
 +
== 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), ..., 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>.
 +
* [[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>.
 +
* 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 ==
 
== See also ==

Revision as of 12:41, 8 November 2008

Addition is the mathematical operation which combines two quantities. The result of addition is called a sum.

Notation

The sum of two numbers $a$ and $b$ is denoted $a+b$, which is read "a plus b." The sum of $f(a), f(a+1), f(a+2), f(a+3), ..., f(b)$, 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 $a+b+c$.
  • 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 $a$.
  • 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)

See also

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS