What is algebraic number? - Definition from WhatIs.com
Part of the Mathematics glossary:

An algebraic number is any real number that is a solution of some single-variable polynomial equation whose coefficient s are all integer s. While this is an abstract notion, theoretical mathematics has potentially far-reaching applications in communications and computer science, especially in data encryption and security.

The general form of a single-variable polynomial equation is:

a + a 1 x + a 2 x 2 + a 3 x 3 + ... + a n x n = 0

where a , a 1 , a 2 , ..., a n are the coefficients, and x is the unknown for which the equation is to be solved. A number x is algebraic if and only if there exists some equation of the above form such that a , a 1 , a 2 , ..., a n are all integers.

All rational number s are algebraic. Examples include 25, 7/9, and -0.245245245. Some irrational number s are also algebraic. Examples are 2 1/2 (the square root of 2) and 3 1/3 (the cube root of 3). There are irrational numbers x for which no single-variable, integer-coefficient polynomial equation exists with x as a solution. Examples are pi (the ratio of a circle's circumference to its diameter in a plane) and e (the natural logarithm base). Numbers of this type are known as transcendental number s.

This was last updated in September 2005
Posted by: Margaret Rouse

Related Terms


  • data-driven decision management (DDDM)

    - Data-driven decision management (DDDM) is an approach to business governance that values actions that can be backed up with verifiable data. The success of a data-driven approach is reliant upon th... (WhatIs.com)

  • continuum

    - A continuum is a continuous system or range in which adjacent elements do not vary from each other in any marked degree although the endpoints of the system may be drastically different. (WhatIs.com)

  • space

    - In mathematics, space is an unbounded continuum (unbroken set of points) in which exactly three numerical coordinates are necessary to uniquely define the location of any particular point. It is so... (WhatIs.com)


  • Mathematics

    - Terms related to mathematics, including definitions about logic, algorithms and computations and mathematical terms used in computer science and business.

  • Internet applications

    - This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

Ask a Question About algebraic numberPowered by ITKnowledgeExchange.com

Get answers from your peers on your most technical challenges

Tech TalkComment



    Contribute to the conversation

    All fields are required. Comments will appear at the bottom of the article.