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, and [[positive integer]], ''n'', there is some positive integer, ''m'' ≤ ''n'' , such that the difference between ''m''α and the nearest integer is at most 1/(''n'' + 1).

For example, no matter what value is chosen for α, at least one of the first five integer multiples of α, namely