Dirichlet's approximation theorem: Difference between revisions

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In [[number theory]], '''Dirichlet's theorem on Diophantine approximation''', also called '''Dirichlet's approximation theorem''', states that for any [[real numbers]] <math> \alpha </math> and <math> N </math>, with <math> 1 \leq N </math>, there existsexist integers <math> p </math> and <math> q </math> such that <math> 1 \leq q \leq N </math> and

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