Recent content by alphabitsabc

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So the equality is that given r > s and x_1, x_2, \ldots x_n \epsilon \; \Re where s \geq 0 if any of the x_1, x_2, \ldots x_n = 0. Then: P(r) \geq P(s) where P(r) = \left \{ {\begin{array}{*{20}c} {(\frac{x_1^r + x_2^r \ldots + x_n^r}{n})^{1/r},} & {r \neq 0} \\...

Hi everyone! So I'm trying to learn more about inequalities and the one I'm starting with is the power means inequality. But it all seems pretty intuitive except how they define the n=0 power mean (i.e. the geometric mean). I read that it's actually the limit as n->0, but I don't see why that's...