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In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real number α and any positive integer ''N'', there exists integers ''p'' and ''q'' such that 1 ≤ ''q'' ≤ ''N'' and : This is a fundamental 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 inequality : is satisfied by infinitely many integers ''p'' and ''q''. This corollary also shows that the Thue–Siegel–Roth theorem, a result in the other direction, provides essentially the tightest possible bound, in the sense that the limits on rational approximation of algebraic numbers cannot be improved by lowering the exponent 2 + ε beyond 2. ==Simultaneous Version== The simultaneous version of the Dirichlet's approximation theorem states that given real numbers and a natural number then there are integers such that 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dirichlet's approximation theorem」の詳細全文を読む スポンサード リンク
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