Number is an abstract concept which is not defined generally in mathematics.  The numbers can be used for counting .

In mathematics one can define different kinds of numbers; some of the most common are .  There are also many special kinds of e.g. : odd numbersMathworldPlanetmathPlanetmath, prime numbersMathworldPlanetmath, triangular numbersMathworldPlanetmath, Fibonacci numbersMathworldPlanetmath, etc.  The algebraic integersMathworldPlanetmath ( are a special kind of complex numbersMathworldPlanetmathPlanetmath, having similar ( divisibility properties as the but much richer.

Usually the numbers, which can be thought to be formed by gradually expanding the available system of numbers:

A usual applier of the mathematics, e.g. an engineer, probably believes that there are no other numbers than the complex numbers.  Some school book may tell that the complex numbers form the widest possible field ( of numbers.  However, the mathematicians know that there exist infinitely many extension fieldsMathworldPlanetmath of the field of the complex numbers, e.g. the rational function fieldPlanetmathPlanetmath (X) or the formal Laurent series field ((X)).  That’s a different matter if one wants to call numbers the elements of the last fields.

The field of the rational numbers can be extended also in another direction than the real and complex numbers:  the field of p-adic numbers ( makes a completion of which resembles but which is not contained neither in in .

Title number
Canonical name Number
Date of creation 2015-11-17 12:09:30
Last modified on 2015-11-17 12:09:30
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Feature
Classification msc 03E10
Related topic ClassificationOfComplexNumbers
Related topic Fraction
Related topic CardinalNumber
Related topic OrdinalNumber
Related topic RuleOfProduct