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Liouville's Inequality
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Definition/Summary
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| The jist of Louiville's Inequality says that rational numbers are poor approximators of irrational algebriac numbers. |
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Recent forum threads on Liouville's Inequality
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Breakdown
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Mathematics
> Calculus/Analysis
>> Inequalities
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Extended explanation
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Let x be an irrational algebraic number and p and q be any integers, with q>0. Then there exists a positive number, K(x) such that
[tex]|x-\frac{p}{q}| > \frac{K(x)}{q^n}[/tex]
where n is the degree of the minimal polynomial of the irrational algebraic number. |
Commentary
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