Kronecker's approximation theorem
GPTKB entity
Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
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| gptkbp:appliesTo |
irrational rotations on the torus
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| gptkbp:category |
theorems in analysis
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| gptkbp:field |
gptkb:Diophantine_approximation
number theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Kronecker's approximation theorem
|
| gptkbp:namedAfter |
gptkb:Leopold_Kronecker
|
| gptkbp:publishedIn |
gptkb:Mathematische_Werke
|
| gptkbp:relatedTo |
gptkb:Weyl's_equidistribution_theorem
|
| gptkbp:sentence |
If α₁, ..., αₙ are real numbers linearly independent over the rationals, then for any real numbers β₁, ..., βₙ and any ε > 0, there exists an integer q and integers p₁, ..., pₙ such that |qαᵢ - pᵢ - βᵢ| < ε for all i.
|
| gptkbp:yearProposed |
1884
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| gptkbp:bfsParent |
gptkb:Kronecker's_theorem
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| gptkbp:bfsLayer |
5
|