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Fungrim entry: 09cd0b

sin(α)Q\sin(\alpha) \notin \overline{\mathbb{Q}}
References:
  • Consequence of the Lindemann-Weierstrass theorem.
Assumptions:αQ{0}\alpha \in \overline{\mathbb{Q}} \setminus \left\{0\right\}
TeX:
\sin(\alpha) \notin \overline{\mathbb{Q}}

\alpha \in \overline{\mathbb{Q}} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
AlgebraicNumbersQ\overline{\mathbb{Q}} Algebraic numbers
Source code for this entry:
Entry(ID("09cd0b"),
    Formula(NotElement(Sin(alpha), AlgebraicNumbers)),
    References("Consequence of the Lindemann-Weierstrass theorem."),
    Variables(alpha),
    Assumptions(Element(alpha, SetMinus(AlgebraicNumbers, Set(0)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC