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Chebyshev's theorem
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'''Chebyshev's theorem''' is any of several theorems proven by Russian mathematician [[Pafnuty Chebyshev]]. * [[Bertrand's postulate]], that for every ''n'' there is a prime between ''n'' and 2''n''. * [[Chebyshev's inequality]], on the range of standard deviations around the mean, in statistics * [[Chebyshev's sum inequality]], about sums and products of decreasing sequences * Chebyshev's [[equioscillation theorem]], on the approximation of continuous functions with polynomials * The statement that if the function <math display=inline>\pi(x)\ln x/x</math> has a limit at infinity, then the limit is 1 (where {{pi}} is the prime-counting function). This result has been superseded by the [[prime number theorem]]. {{mathdab}}
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