An irrational number is one that cannot be written as *a* / *b* with both *a* and *b* integers. A great many naturally occurring numbers, such as , e, and π, are irrational. The following proof that is irrational is one of the best-known arguments in all of mathematics. Suppose that = *a* / *b*; since common factors can be canceled, we may assume that *a* and *b* have no common factor; we have *a*^{2} = 2*b*^{2}, which ...

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