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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 |
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=== Theorems === | === Theorems === | ||
- | AM-GM inequality. | + | Inequality of arithmetic and geometric means (AM-GM inequality): |
- | $\dfrac{1}{n}\sum_{k=1}^n x_k \ge \left(\prod_{k=1}^n x_k\right)^\frac{1}{n}$ | + | ^ $\frac{1}{n}\sum_{k=1}^n x_k \ge \left(\prod_{k=1}^n x_k\right)^\frac{1}{n}$ ^ |
=== 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]] | ||
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