Chebyshev's theorem explained

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 2n.
• 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 $\backslash pi(x)\backslash ln\; x/x$ has a limit at infinity, then the limit is 1 (where is the prime-counting function). This result has been superseded by the prime number theorem.