$\mathop{\operatorname{arg\,min}}\limits_{x \in \mathbb{R}} \left[\sin\!\left(x\right)\right] = \left\{ \pi \left(2 n - \frac{1}{2}\right) : n \in \mathbb{Z} \right\}$
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
ArgMin$\mathop{\operatorname{arg\,min}}\limits_{P\left(x\right)} f\!\left(x\right)$ Locations of minimum value
Sin$\sin\!\left(z\right)$ Sine
RR$\mathbb{R}$ Real numbers
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ConstPi$\pi$ The constant pi (3.14...)
ZZ$\mathbb{Z}$ 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)))))

## Topics using this entry

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