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Line 3: :<math> \left \| q \alpha -p \right \| \le \frac{1}{N+1} </math> This is a foundational result in [[~~diophantine~~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 inequality :<math> \left \| \alpha -\frac{p}{q} \right \| < \frac{1}{q^2} </math>

Dirichlet's approximation theorem: Difference between revisions