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irrational number
In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.
When the ratio of lengths of two line segments is irrational, the line segments are also described as being ''incommensurable'', meaning they share no measure in common.
Numbers which are irrational include the ratio of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two;〔(The 15 Most Famous Transcendental Numbers ). by Clifford A. Pickover. URL retrieved 24 October 2007.〕〔http://www.mathsisfun.com/irrational-numbers.html; URL retrieved 24 October 2007.〕〔 URL retrieved 26 October 2007.〕 in fact all square roots of natural numbers, other than of perfect squares, are irrational.
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抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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