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The Math Kanji (数学の漢字)

Recently I was studying some kanji when I noticed that the kanji 数 is used to express a wide variety of mathematical terminology. I thought it would be interesting to write a little bit about how this kanji is used.

最近、漢字を勉強する時は色々な数学的の用語を表すために「数」が使われるのことに気づいた。この漢字の使い方について少し書くのが面白いと思った。

Disclaimer: I have not read any mathematical texts in Japanese, and am relying on terms as found in my Kanji Dictionary along with my own knowledge.

免責:日本語で数学の論文を読むのことがなくて漢字辞書の言葉と私の知識を使っています。

The Meaning of 数

The dictionary definition of this kanji along with all of its readings can be found here. On its own, this kanji is commonly read as:

  • すう:suu, used as a prefix to refer to an arbitrary amount of something (can be a few or several), or as a suffix meaning “the number of” something.
  • かず:kazu, a noun meaning number or amount.
  • 数える(かぞえる):kazoeru, a verb meaning to count.

For example, if you wanted to say something like “the number of plates” in Japanese, you could say 皿の数 (sara no kazu), or you could say 皿数 (sarasuu). “A few plates” would then be 数皿 (suusara), while “counting plates” would be 皿を数える (sara wo kazoeru).

Mathematical Terminology

Being closely related to numbers, 数 is used in the terms for common types of numbers, such as:

  • 正数(せいすう):seisuu, positive numbers
  • 負数(ふすう):fusuu, negative numbers
  • 偶数(ぐうすう):guusuu, even numbers
  • 奇数(きすう):kisuu, odd numbers
  • 整数(せいすう):seisuu, integers (watch the kanji!)
  • 自然数(しぜんすう):shizensuu, natural numbers
  • 有理数(ゆうりすう):yuurisuu, rational numbers
  • 無理数(むりすう):murisuu, irrational numbers
  • 実数(じっすう):jissuu, real numbers
  • 虚数(きょすう):kyosuu, imaginary numbers
  • 素数(そすう):sosuu, prime numbers
  • 完全数(かんぜんすう): kanzensuu, perfect numbers

This kanji also appears in terms describing fractions and decimal numbers:

  • 小数(しょうすう):shousuu, decimal
    • 小数点(しょうすうてん):shousuuten, decimal point
  • 分数(ぶんすう):bunsuu, fraction
    • 真分数(しんぶんすう):shinbunsuu, proper fraction
    • 仮分数(かぶんすう):kabunsuu, improper fraction
    • 帯分数(たいぶんすう):taibunsuu, mixed fraction
  • 端数(はすう):hasuu, fractional part
  • 逆数(ぎゃくすう):gyakusuu, reciprocal
  • 除数(じょすう):josuu, divisor

With types of numbers out of the way, we now move on to algebra. In Japanese, algebra is 代数 (daisuu); in a more literal sense this can be translated as “number substitution”, which is certainly something you do when starting out!

  • 函数(かんすう):kansuu, function (can also be written as 関数 with no change in pronunciation)
    • 対数(たいすう):taisuu, logarithm
  • 係数(けいすう):keisuu, coefficient
  • 変数(へんすう):hensuu, variable
  • 定数(ていすう):teisuu, constant
  • 指数(しすう):shisuu, exponent
  • 次数(じすう):jisuu, degree

And now for some things a little bit past high school algebra:

  • 数列 (すうれつ):suuretsu, progression or sequence
  • 級数(きゅうすう):kyuusuu, series
    • 等比級数(とうひきゅうすう):touhi kyuusuu, geometric series
    • 等差級数(とうさきゅうすう):tousa kyuusuu, arithmetic series

Counting

As mentioned before, if you want to say you are counting, you use the verb 数える. However, if you want to express the actual count of something, you need to use a counter word (Wikipedia has a pretty good article on Japanese counter words found here). Common counters include 人 for people (usually read as nin), 分 for minutes (usually read as fun, but pronounced more like foon), and 歳 for age (read as sai), though there exist many different counters for different types of objects and entities.

Using what I mentioned previously, you could say 皿の数は5です to say “There are five plates”, though more literally this sentence would sound like “The number of plates is five”. A more natural way of saying this would be 皿が五枚あります (Sara ga gomai arimasu), where we use the counter 枚 for flat objects such as plates. More generally, you can use generic counters such as 一つ (hitotsu - one) and 二つ (futatsu - two) if you’re not sure which counter to use.

Conclusion

Even though most of this content isn’t particularly useful unless you plan on studying mathematics in Japan, knowing how to count and express the numbers of things is an important skill to have. In future foreign language posts I will definitely try to avoid just listing a bunch of words like I did in this article, and instead focus more on actually writing and expressing ideas.