Lindemann–Weierstrass theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
theorems in algebra
theorems in number theory |
| gptkbp:field |
number theory
transcendental number theory |
| gptkbp:generalizes |
gptkb:Gelfond–Schneider_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lindemann–Weierstrass theorem
|
| gptkbp:implies |
e is transcendental
π is transcendental |
| gptkbp:namedAfter |
gptkb:Ferdinand_von_Lindemann
gptkb:Karl_Weierstrass |
| gptkbp:provenBy |
gptkb:Ferdinand_von_Lindemann
|
| gptkbp:publishedIn |
1885
|
| gptkbp:relatedTo |
gptkb:Hermite–Lindemann_theorem
|
| gptkbp:state |
If α₁, ..., αₙ are distinct algebraic numbers, then e^{α₁}, ..., e^{αₙ} are linearly independent over the algebraic numbers.
|
| gptkbp:bfsParent |
gptkb:Transcendental_number_theory
gptkb:Schanuel's_conjecture |
| gptkbp:bfsLayer |
8
|