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Liouville's Inequality

 Definition/Summary The jist of Louiville's Inequality says that rational numbers are poor approximators of irrational algebriac numbers.

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 Breakdown Mathematics > Calculus/Analysis >> Inequalities

 Extended explanation 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 $$|x-\frac{p}{q}| > \frac{K(x)}{q^n}$$ where n is the degree of the minimal polynomial of the irrational algebraic number.