natural numbers

natural numbers

English

Noun

natural numbers pl (normally plural, singular natural number)

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: 自然数 (ziranshu) 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)

Korean: 자연수(自然數, jayeonsu) 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.