Irrational numbers

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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 fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal, binary, etc.) never ends and never enters a periodic pattern. "Almost all" real numbers are irrational, in a sense which is defined more precisely below.