Fungrim entry: ad04bd

\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

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