# Differences

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 order_structure_of_real_numbers [2015/06/30 16:11]nikolaj order_structure_of_real_numbers [2015/06/30 16:14]nikolaj Both sides previous revision Previous revision 2015/06/30 16:14 nikolaj 2015/06/30 16:12 nikolaj 2015/06/30 16:11 nikolaj 2015/06/30 16:11 nikolaj 2014/03/21 11:11 external edit2013/09/08 15:00 nikolaj 2013/09/08 14:58 nikolaj created Next revision Previous revision 2015/06/30 16:14 nikolaj 2015/06/30 16:12 nikolaj 2015/06/30 16:11 nikolaj 2015/06/30 16:11 nikolaj 2014/03/21 11:11 external edit2013/09/08 15:00 nikolaj 2013/09/08 14:58 nikolaj created Line 9: Line 9: ----- ----- === Theorems === === Theorems === - AM-GM inequality. + Inequality of arithmetic and geometric means (AM-GM inequality): - $\dfrac{\sum_{k=1}^n x_k}{n} \ge \left(\prod_{k=1}^n x_k\right)^\frac{1}{n}$ + ^ $\frac{1}{n}\sum_{k=1}^n x_k \ge \left(\prod_{k=1}^n x_k\right)^\frac{1}{n}$ ​^ === Reference === === Reference === - Wikipedia: [[http://​en.wikipedia.org/​wiki/​Real_number|Real number]], [[http://​en.wikipedia.org/​wiki/​Construction_of_the_real_numbers|Construction of the real numbers]], [[http://​en.wikipedia.org/​wiki/​Dedekind_cut|Dedekind cut]] + Wikipedia: ​ + [[http://​en.wikipedia.org/​wiki/​Real_number|Real number]], ​ + [[http://​en.wikipedia.org/​wiki/​Construction_of_the_real_numbers|Construction of the real numbers]], ​ + [[http://​en.wikipedia.org/​wiki/​Dedekind_cut|Dedekind cut]], + [[https://​en.wikipedia.org/​wiki/​Inequality_of_arithmetic_and_geometric_means|Inequality of arithmetic and geometric means]] ----- -----