Fungrim entry: 09cd0b

\sin\!\left(\alpha\right) \notin \overline{\mathbb{Q}}

References:

Consequence of the Lindemann-Weierstrass theorem.

Assumptions:

\alpha \in \overline{\mathbb{Q}} \setminus \left\{0\right\}

TeX:

\sin\!\left(\alpha\right) \notin \overline{\mathbb{Q}}

\alpha \in \overline{\mathbb{Q}} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin\!\left(z\right)$	Sine
`AlgebraicNumbers`	$\overline{\mathbb{Q}}$	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)))))

Topics using this entry

Sine

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

2019-06-18 07:49:59.356594 UTC