Dirichlet's approximation theorem
GPTKB entity
Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:field |
number theory
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| gptkbp:generalizes |
gptkb:Minkowski's_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dirichlet's approximation theorem
|
| gptkbp:implies |
existence of good rational approximations to real numbers
|
| gptkbp:namedAfter |
gptkb:Peter_Gustav_Lejeune_Dirichlet
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| gptkbp:publishedIn |
19th century
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| gptkbp:relatedTo |
gptkb:Kronecker's_theorem
gptkb:Diophantine_approximation |
| gptkbp:sentence |
For any real number α and any positive integer N, there exist integers p and q with 1 ≤ q ≤ N such that |αq − p| < 1/N.
|
| gptkbp:usedIn |
proof of irrationality of certain numbers
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| gptkbp:bfsParent |
gptkb:Diophantine_approximation
gptkb:Johann_Peter_Gustav_Lejeune_Dirichlet |
| gptkbp:bfsLayer |
6
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