Algebraic number
Revision as of 20:19, 24 April 2008 by I like pie (talk | contribs)
An algebraic number is a root of a polynomial with integer coefficients. Examples include 
, 
, 
, and ![$\frac{4+\sqrt[27]{19}}{\sqrt[3]{4}+\sqrt[7]{97}}$](http://latex.artofproblemsolving.com/f/b/2/fb23020f8042aef7ccbbf8d8585c78fcb421adef.png)
. A number that is not algebraic is called a transcendental number, such as 
and 
.
Number of algebraic numbers
Although it seems that the number of algebraic numbers is large, there are only countably many of them. That is, the algebraic numbers have the same cardinality as the integers.
Algebraic numbers are studied extensively in algebraic number theory.
This article is a stub. Help us out by expanding it.
