Dirichlet's approximation theorem: Difference between revisions

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In [[mathematics]], '''Dirichlet's theorem''' on [[diophantine approximation]] ('''Dirichlet's approximation theorem''') states that for any [[real number]] α, some integer multiple

:''m''α or −:''m''α

has relatively small [[fractional part]] (in other words, the multiples of α can't stay too far away from integers). In quantitative terms, the fractional partdifference of one of the first ''N'' multiples and some integer must take a value at most

:1/(''N'' + 1).