“rational number”的概念、定义、习题解题方法及翻译-数学辞典

单词

rational number

释义

rational number

A number that can be written in the form a/b, where a and b are integers, with b ≠ 0. The set of all rational numbers is usually denoted by ℚ. A real number is rational if and only if, when expressed as a decimal, it has a finite or recurring expansion (see decimal representation). For example,

A famous proof, attributed to Pythagoras, shows that $inline$ is not rational, and e and π are also known to be irrational.

The same rational number can be expressed as a/b in different ways; for example, $inline$ In fact, a/b = c/d if and only if ad = bc. But a rational number can be expressed uniquely as a/b if it is insisted that a and b are coprime and that b>0. The field ℚ is the field of fractions of the ring of integers ℤ.

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