Difference between revisions of "Binary operation"

From Citizendium
Jump to navigation Jump to search
imported>Richard Pinch
(new entry, just a stub)
 
imported>David E. Volk
m (subpages)
Line 1: Line 1:
{{subpages}}
In [[mathematics]], a '''binary operation''' on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the [[arithmetic]] and [[elementary algebra]]ic operations of addition, subtraction, multiplication and division.
In [[mathematics]], a '''binary operation''' on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the [[arithmetic]] and [[elementary algebra]]ic operations of addition, subtraction, multiplication and division.



Revision as of 12:41, 28 November 2008

This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

In mathematics, a binary operation on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the arithmetic and elementary algebraic operations of addition, subtraction, multiplication and division.

Formally, a binary operation on a set S is a function on the Cartesian product

given by

using operator notation rather than functional notation, which would call for writing .

Properties

A binary operation may satisfy further conditions.

  • Commutative:
  • Associative:
  • Alternative:
  • Power-associative:

Special elements which may be associated with a binary operations include:

  • Neutral element I: for all x
  • Absorbing element O: for all x