# Number System - Natural Numbers (cardinal and ordinal numbers) - <math>\mathbb{N} </math>

### Table of Contents

## About

A natural number <math>\mathbb{N} </math> can be used for two purposes:

- to count (ie describe the size of a set)
- to order (ie or to describe the position of an element in a sequence).

`0, 1, 2, 3, 4, ... or 1, 2, 3, 4, `

The natural numbers are those used for:

Operation | Example | Words |
---|---|---|

counting | there are six coins on the table | cardinal numbers |

ranking | this is the third largest city in the country | ordinal numbers |

## Articles Related

## Number systems

## Representation

### Symbol

In the base 10 numeral system, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

### Class

In set theory, natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three elements.