Algebraic number
From AoPSWiki
A complex number is said to be algebraic if it is a root of a polynomial with rational coefficients. Examples include 
, 
, 
, and ![\frac{4+\sqrt[27]{19}}{\sqrt[3]{4}+\sqrt[7]{97}}](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/e/c/7/ec7795f1168814cdd4f58b68c98b9e9c82b4b085.gif "Click on the formula to view the LaTeX code")
. 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.
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