"Lindemann-Weierstrass theorem" meaning in All languages combined

{
  "etymology_text": "Named after Ferdinand von Lindemann and Karl Weierstrass, who worked on related proofs.",
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        "A result that is useful in establishing the transcendence of numbers, stating that, if α₁, ..., αₙ are algebraic numbers which are linearly independent over the rational numbers ℚ, then e^(α₁), ..., e^(αₙ) are algebraically independent over ℚ."
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        "(number theory) A result that is useful in establishing the transcendence of numbers, stating that, if α₁, ..., αₙ are algebraic numbers which are linearly independent over the rational numbers ℚ, then e^(α₁), ..., e^(αₙ) are algebraically independent over ℚ."
      ],
      "synonyms": [
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          "word": "Weierstrass-Lindemann theorem"
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        "Lindemann-Weierstrass theorem"
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  "word": "Lindemann-Weierstrass theorem"
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  "etymology_text": "Named after Ferdinand von Lindemann and Karl Weierstrass, who worked on related proofs.",
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        "A result that is useful in establishing the transcendence of numbers, stating that, if α₁, ..., αₙ are algebraic numbers which are linearly independent over the rational numbers ℚ, then e^(α₁), ..., e^(αₙ) are algebraically independent over ℚ."
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      "raw_glosses": [
        "(number theory) A result that is useful in establishing the transcendence of numbers, stating that, if α₁, ..., αₙ are algebraic numbers which are linearly independent over the rational numbers ℚ, then e^(α₁), ..., e^(αₙ) are algebraically independent over ℚ."
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