# Natural Number

A Natural Number is either an N0 Natural Number or an N1 Natural Number.

## References

### 2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Natural_number
• In mathematics, a natural number means either an element of the set {1, 2, 3, ...} (the positive integers) or an element of the set {0, 1, 2, 3, ...} (the non-negative integers).
• Natural numbers have two main purposes: counting ("there are 3 apples on the table") and ordering ("this is the 3rd largest city in the country").
• Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting, such as Ramsey theory, are studied in combinatorics.
• Mathematicians use N or \mathbb{N} (an N in blackboard bold, displayed as ℕ in Unicode) to refer to the set of all natural numbers. This set is countably infinite: it is infinite but countable by definition. This is also expressed by saying that the cardinal number of the set is aleph-null (\aleph_0).
• To be unambiguous about whether zero is included or not, sometimes an index "0" is added in the former case, and a superscript "*" or subscript "1" is added in the latter case:
• \mathbb{N}_0 = \{ 0, 1, 2, \ldots \}; \quad \mathbb{N}^* = \mathbb{N}_1 = \{ 1, 2, \ldots \}.
• WordNet http://wordnet.princeton.edu/perl/webwn?s=natural%20number
• the number 1 and any other number obtained by adding 1 to it repeatedly