V2EX rational number

Rational Number

Definition / 释义

有理数:能表示为两个整数之比 \( \frac{p}{q} \)(其中 \(p, q\) 为整数且 \(q \neq 0\))的数。它包括整数、有限小数和无限循环小数。(另外还有“理性的、合乎理性”的 rational 作形容词的用法,此处主要指数学概念。)

Pronunciation (IPA) / 发音(IPA)

/rnl nmbr/

Examples / 例句

A fraction is a rational number.
分数是一种有理数。

Although \( \sqrt{2} \) is not a rational number, it can be approximated by rational numbers like \( \frac{99}{70} \).
虽然 \( \sqrt{2} \) 不是有理数,但它可以用 \( \frac{99}{70} \) 这类有理数来近似。

Etymology / 词源

rational 来自拉丁语 rationalis(“理性的、可用理性解释的”),与 ratio(“比、比例、推理”)同源;在数学里强调“能用比例(比)表示”。number 来自拉丁语 numerus(“数、数量”)。因此 rational number 字面上可理解为“能用比例(两个整数之比)表示的数”。

Related Words / 相关词汇

Literary Works / 文学与著作中的用例

  • Euclid Elements(《几何原本》):以“比例/比”(ratio)为核心思想,为“可用整数比表达”的数的观念奠基(现代文本常用 rational numbers 归纳这类对象)。
  • Richard Courant & Herbert Robbins *What Is Mathematics?*(《什么是数学》):讨论数系扩张时会系统对比 rational numbersirrational numbers
  • Tom M. Apostol Calculus(《微积分》):在实数、数轴与稠密性等内容中常出现 rational number(s) 的表述与性质。
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