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## real numbers |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

The set of all (finite and infinite) decimal numbers is referred to as real numbers. Real numbers can be identified with the points of the real line. A number corresponds to the distance from the origin, while its algebraic sign indicates whether belongs to the positive or negative half line.

The rational numbers are dense in , that is every irrational number can be approximated by fractions to an arbitrary degree of accuracy. Unlike however, is not countable.

Together with addition and multiplication, the real numbers form a field. Moreover, is complete, that is every convergent sequence of real numbers has a limit in .

(Authors: Höllig/Kopf/Abele)

**Annotation:**

- Cantorsches Diagonalverfahren (german)

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automatically generated 6/11/2007 |