# Difference between revisions of "Algebraic number"

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− | An '''algebraic number''' is a [[root]] of a [[polynomial]] with [[integer]] [[coefficient]]s. Examples include <math>\frac{1}{3}</math>, <math>\sqrt{2}+\sqrt{3}</math>, <math> | + | An '''algebraic number''' is a [[root]] of a [[polynomial]] with [[integer]] [[coefficient]]s. Examples include <math>\frac{1}{3}</math>, <math>\sqrt{2}+\sqrt{3}</math>, <math>\imath</math>, and <math>\frac{4+\sqrt[27]{19}}{\sqrt[3]{4}+\sqrt[7]{97}}</math>. A number that is not algebraic is called a [[transcendental number]]. Examples of transcendental numbers are <math>e</math> and <math>\pi</math>. |

## Revision as of 23:24, 30 October 2006

An **algebraic number** is a root of a polynomial with integer coefficients. Examples include , , , and . A number that is not algebraic is called a transcendental number. Examples of transcendental numbers are and .

### Number of algebraic numbers

Although it initially seems that the number of algebraic numbers is large, it turns out that 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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