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Irrational number

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In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a ratio of two integers, i.e., it is not of the form

[math]\displaystyle{ \Large \frac{a}{b} }[/math]

where [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] are integers and [math]\displaystyle{ b }[/math] is not zero. It can readily be shown that the irrational numbers are precisely those numbers whose expansion in any given base (decimal, binary, etc) never ends and never enters a periodic pattern, but no mathematician takes that to be a definition. Some examples of irrational numbers are [math]\displaystyle{ \sqrt{2} }[/math] or [math]\displaystyle{ e }[/math].

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