FACTOID # 25: If you're tired of sitting in traffic on your way to work, move to North Dakota.
 
 Home   Encyclopedia   Statistics   States A-Z   Flags   Maps   FAQ   About 
   
 
WHAT'S NEW
 

SEARCH ALL

FACTS & STATISTICS    Advanced view

Search encyclopedia, statistics and forums:

 

 

(* = Graphable)

 

 


Encyclopedia > Binary operations

In mathematics, a binary operation, or binary operator, is a calculation involving two input quantities and one kind of a specific operation. It is sometimes called a dyadic operation as well. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division.


More precisely, a binary operation on a set S is a binary function from S and S to S, in other words a function f from the Cartesian product S S to S. Sometimes, especially in computer science, the term is used for any binary function. That f takes values in the same set S that provides its arguments is the property of closure.


Binary operations are the keystone of algebraic structures studied in abstract algebra: they form part of groups, monoids, semigroups, rings, and more. Most generally, a magma is a set together with any binary operation defined on it.


Many binary operations of interest are commutative or associative. Many also have identity elements and inverse elements. Typical examples of binary operations are the addition (+) and multiplication (*) of numbers and matrices as well as composition of functions on a single set.


Examples of operations that are not commutative are subtraction (-), division (/), exponentiation(^), and super_exponentiation(@).


Binary operations are often written using infix notation such as a * b, a + b, or a b rather than by functional notation of the form f(a,b). Sometimes they are even written just by juxtaposition: ab. They can also be expressed using prefix or postfix notations. A prefix notation, Polish notation, dispenses with parentheses; it is probably more often encountered now in its postfix form, reverse Polish notation.


External binary operations

An external binary operation is a binary function from K and S to S. This differs from a binary operation in the strict sense in that K need not be S; its elements come from outside.


An example of an external binary operation is scalar multiplication in linear algebra. Here K is a field and S is a vector space over that field.


An external binary operation may alternatively be viewed as an action; K is acting on S.






  Results from FactBites:
 
Encyclopedia4U - Binary operation - Encyclopedia Article (395 words)
In mathematics, a binary operation, or binary operator, is a calculation involving two input quantities and one kind of a specific operation.
Binary operations are the keystone of algebraic structures studied in abstract algebra: they form part of groups, monoids, semigroups, ringss, and more.
Binary operations are often written using infix notation such as a * b, a + b, or a · b rather than by functional notation of the form f(a,b).
Binary operation - Wikipedia, the free encyclopedia (410 words)
Binary operations are the keystone of algebraic structures studied in abstract algebra: they form part of groups, monoids, semigroups, rings, and more.
Many binary operations of interest in both algebra and formal logic are commutative or associative.
Typical examples of binary operations are the addition (+) and multiplication (*) of numbers and matrices as well as composition of functions on a single set.
  More results at FactBites »

 
 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your comments

Want to know more?
Search encyclopedia, statistics and forums:

 


Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 1022, m