Monthly Archives: January 2014

A short proof of Chebyshev’s inequality


A proof from my book. This theorem was needed to estimate (from below) the growth function of Okninski’s semigroup. For every natural number let ¬†¬†denote the number of primes . Say, , , , etc. The next theorem was proved by Chebyshev in 1850. We present a proof based on some ideas of Erdos (he […]