References:
- Niven's theorem
TeX:
\left(x \in \mathbb{Q} \,\mathbin{\operatorname{and}}\, \sin\!\left(\pi x\right) \in \mathbb{Q}\right) \implies \left(\sin\!\left(\pi x\right) \in \left\{0, \frac{1}{2}, -\frac{1}{2}, 1, -1\right\}\right)
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
Rational numbers | ||
Sin | Sine | |
ConstPi | The constant pi (3.14...) |
Source code for this entry:
Entry(ID("056c0e"), Formula(Implies(And(Element(x, QQ), Element(Sin(Mul(ConstPi, x)), QQ)), Element(Sin(Mul(ConstPi, x)), Set(0, Div(1, 2), Neg(Div(1, 2)), 1, -1)))), References("Niven's theorem"))