natural numbers

English

Noun

1. (mathematics) The set of positive integers, {1, 2, 3, ...}.
2. (mathematics, computer science) The set of non-negative integers, {0, 1, 2, 3, ...}.

Usage notes

In computer science, the natural numbers always include zero. In mathematics, some texts define them to include zero and some do not.

Synonyms

• counting numbers (positive integers)
• whole numbers (either sense)
• ℕ

Related terms

• set
• natural number
• inductive definition

Translations

number theory

• Chinese: 自然數／自然数 (zìránshù)
• Dutch: natuurlijk getal (nl) n
• Finnish: luonnolliset luvut, luonnollisten lukujen joukko
• German: natürliche Zahlen (de) f pl
• Italian: numero naturale (it) m
• Japanese: 自然数 (ja) (しぜんすう, shizensu)
• (deprecated template usage) {{trans-mid}}
• Korean: 자연수 (ko) (jayeonsu) (自然數 (ko))
• Portuguese: números naturais
• Russian: натуральные числа pl (naturalʹnyje čisla)
• Swedish: naturliga tal n pl
• Telugu: సహజ సంఖ్యలు (sahaja saṅkhyalu)

References

• “natural number”, in Dictionary.com Unabridged, Dictionary.com, LLC, 1995–present.
• “natural number”, in The American Heritage Dictionary of the English Language, 4th edition, Boston, Mass.: Houghton Mifflin, 2000, →ISBN.
• "natural number" in WordNet 2.0, Princeton University, 2003.