Recitation 2

After introducing Triangle Inequality and Arithmetic Geometric Mean Inequality, I briefly discussed a more general way to define means. For any ‘good enough’ function f, the mean value of x, y generated by f can be defined as f^{-1}\left(\frac{f(x)+f(y)}{2}\right). The identity map gives rise to the arithmetic mean A, the natural log the geometric mean G, the reciprocal function the harmonic mean H, and the square function the root mean square S. And all of those mean values are related by the following inequality chains, H \leq G\leq A\leq S.

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