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Fungrim entry: ad04bd

arg minxR[sin ⁣(x)]={π(2n12):nZ}\mathop{\operatorname{arg\,min}}\limits_{x \in \mathbb{R}} \left[\sin\!\left(x\right)\right] = \left\{ \pi \left(2 n - \frac{1}{2}\right) : n \in \mathbb{Z} \right\}
TeX:
\mathop{\operatorname{arg\,min}}\limits_{x \in \mathbb{R}} \left[\sin\!\left(x\right)\right] = \left\{ \pi \left(2 n - \frac{1}{2}\right) : n \in \mathbb{Z} \right\}
Definitions:
Fungrim symbol Notation Short description
ArgMinarg minP(x)f ⁣(x)\mathop{\operatorname{arg\,min}}\limits_{P\left(x\right)} f\!\left(x\right) Locations of minimum value
Sinsin ⁣(z)\sin\!\left(z\right) Sine
RRR\mathbb{R} Real numbers
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ConstPiπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("ad04bd"),
    Formula(Equal(ArgMin(Brackets(Sin(x)), x, Element(x, RR)), SetBuilder(Mul(ConstPi, Sub(Mul(2, n), Div(1, 2))), n, Element(n, ZZ)))))

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

2019-08-25 15:30:03.056001 UTC