自然数(しぜんすう)

しぜんすう
noun
natural number (math); counting number
1. in mathematics, a positive whole number used for counting, beginning with 1 and continuing 2, 3, 4, ... without end; a natural number
A standard mathematical term for the set of positive whole numbers 1, 2, 3, ...}. In Japanese school mathematics, zero is not included in the natural numbers — a convention that follows the older European tradition. (This differs from the modern set-theoretic convention in some countries, where natural numbers begin with 0.) The natural numbers are introduced in elementary school and later contrasted with {整数(せいすう) (integers), 有理数(ゆうりすう) (rational numbers), 実数(じっすう) (real numbers), and 複素数(ふくそすう) (complex numbers) as the number system is progressively extended.
一(いち)から始(はじ)まる数(かず)を自然数(しぜんすう)と言(い)う。
Numbers starting from one are called natural numbers.
自然数(しぜんすう)は無限(むげん)に存在(そんざい)する。
There are infinitely many natural numbers.
二(に)つの自然数(しぜんすう)の和(わ)は、かならず自然数(しぜんすう)になる。
The sum of two natural numbers is always a natural number.
日本(にほん)の学校数学(がっこうすうがく)では、自然数(しぜんすう)に零(れい)を含(ふく)めないのが一般的(いっぱんてき)だ。
In Japanese school mathematics, it is standard not to include zero in the natural numbers.

Composed of 自然(しぜん) (natural) + 数(すう) (number). Literally 'natural number,' the Japanese term is a direct calque of the European mathematical term. The idea is that these are the numbers that 'occur naturally' when counting physical objects, before the abstract concepts of zero, negatives, and fractions are introduced.

COMMON COLLOCATIONS:

  • 自然数(しぜんすう)の集合(しゅうごう): the set of natural numbers
  • 自然数(しぜんすう)全体(ぜんたい): all natural numbers (as a set)
  • 正(せい)の自然数(しぜんすう): positive natural number (a pleonasm, since natural numbers are already positive in Japanese convention)
  • 任意(にんい)の自然数(しぜんすう) n: any natural number n (standard phrasing in math proofs)
  • 最小(さいしょう)の自然数(しぜんすう): the smallest natural number (=1 in Japanese convention)

NUMBER SYSTEMS (FROM SMALLEST TO LARGEST):

  • 自然数(しぜんすう): natural numbers — 1, 2, 3, ...
  • 整数(せいすう): integers — ..., -2, -1, 0, 1, 2, ...
  • 有理数(ゆうりすう): rational numbers — any number expressible as a fraction a/b.
  • 無理数(むりすう): irrational numbers — such as √2 and π, which cannot be expressed as fractions.
  • 実数(じっすう): real numbers — all rational and irrational numbers combined.
  • 複素数(ふくそすう): complex numbers — numbers of the form a + bi, including imaginary numbers.

USAGE NOTE:
In Japanese elementary and secondary school mathematics, the 自然数(しぜんすう) conventionally begin with 1 and do not include 0. This is the convention followed by most Japanese textbooks. Some areas of university mathematics (especially those using set theory and computer science) instead define 自然数(しぜんすう) to include 0 — so in advanced contexts the definition should be specified explicitly.

REGISTER:
Neutral but technical. Used almost exclusively in mathematical contexts (classrooms, textbooks, exams, and research). Unlike 整数(せいすう), it is not commonly used figuratively in everyday conversation.

general
Added 2026.4.12 9:57
23000/23397_shizensuu