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- Lindemann–Weierstrass_theorem abstract "In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α1, ..., αn are algebraic numbers which are linearly independent over the rational numbers Q, then eα1, ..., eαn are algebraically independent over Q; in other words the extension field Q(eα1, ..., eαn) has transcendence degree n over Q.An equivalent formulation (Baker 1975, Chapter 1, Theorem 1.4), is the following: If α1, ..., αn are distinct algebraic numbers, then the exponentials eα1, ..., eαn are linearly independent over the algebraic numbers. This equivalence transforms a linear relation over the algebraic numbers into an algebraic relation over the Q by using the fact that a symmetric polynomial whose arguments are all conjugates of one another gives a rational number.The theorem is named for Ferdinand von Lindemann and Karl Weierstrass. Lindemann proved in 1882 that eα is transcendental for every non-zero algebraic number α, thereby establishing that π is transcendental (see below). Weierstrass proved the above more general statement in 1885.The theorem, along with the Gelfond–Schneider theorem, is extended by Baker's theorem, and all of these are further generalized by Schanuel's conjecture.".
- Lindemann–Weierstrass_theorem wikiPageID "348976".
- Lindemann–Weierstrass_theorem wikiPageRevisionID "587992106".
- Lindemann–Weierstrass_theorem subject Category:Articles_containing_proofs.
- Lindemann–Weierstrass_theorem subject Category:E_(mathematical_constant).
- Lindemann–Weierstrass_theorem subject Category:Exponentials.
- Lindemann–Weierstrass_theorem subject Category:Number_theory.
- Lindemann–Weierstrass_theorem subject Category:Pi.
- Lindemann–Weierstrass_theorem subject Category:Theorems_in_number_theory.
- Lindemann–Weierstrass_theorem subject Category:Transcendental_numbers.
- Lindemann–Weierstrass_theorem comment "In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers.".
- Lindemann–Weierstrass_theorem label "Lindemann–Weierstrass theorem".
- Lindemann–Weierstrass_theorem label "Satz von Lindemann-Weierstraß".
- Lindemann–Weierstrass_theorem label "Stelling van Lindemann-Weierstrass".
- Lindemann–Weierstrass_theorem label "Teorema de Lindemann–Weierstrass".
- Lindemann–Weierstrass_theorem label "Teorema de Lindemann–Weierstrass".
- Lindemann–Weierstrass_theorem label "Teorema di Lindemann-Weierstrass".
- Lindemann–Weierstrass_theorem label "Théorème de Lindemann-Weierstrass".
- Lindemann–Weierstrass_theorem label "Теорема Линдемана — Вейерштрасса".
- Lindemann–Weierstrass_theorem label "リンデマンの定理".
- Lindemann–Weierstrass_theorem label "林德曼-魏尔斯特拉斯定理".
- Lindemann–Weierstrass_theorem sameAs Lindemann%E2%80%93Weierstrass_theorem.
- Lindemann–Weierstrass_theorem sameAs Satz_von_Lindemann-Weierstraß.
- Lindemann–Weierstrass_theorem sameAs Teorema_de_Lindemann–Weierstrass.
- Lindemann–Weierstrass_theorem sameAs Théorème_de_Lindemann-Weierstrass.
- Lindemann–Weierstrass_theorem sameAs Teorema_di_Lindemann-Weierstrass.
- Lindemann–Weierstrass_theorem sameAs リンデマンの定理.
- Lindemann–Weierstrass_theorem sameAs Stelling_van_Lindemann-Weierstrass.
- Lindemann–Weierstrass_theorem sameAs Teorema_de_Lindemann–Weierstrass.
- Lindemann–Weierstrass_theorem sameAs Q1572474.
- Lindemann–Weierstrass_theorem sameAs Q1572474.
- Lindemann–Weierstrass_theorem wasDerivedFrom Lindemann–Weierstrass_theorem?oldid=587992106.