Dirichlet's approximation theorem: Difference between revisions

Revision as of 17:35, 5 February 2010

Revision as of 01:17, 19 February 2010

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:<math> \left| q \alpha -p \right| < \frac{1}{N+1} </math>

This is a foundational result in [[diophantine approximation]], showing that any real number has a sequence of good rational approximations: in fact an immediate consequence is that for a given irrational α, the equationinequality

:<math> \left| \alpha -\frac{p}{q} \right| < \frac{1}{q^2} </math>