Fungrim entry: 466095

\left|\operatorname{atan}\!\left(x\right)\right| \le \left|x\right|

Assumptions:

x \in \mathbb{R} \cup \left\{-\infty, \infty\right\}

TeX:

\left|\operatorname{atan}\!\left(x\right)\right| \le \left|x\right|

x \in \mathbb{R} \cup \left\{-\infty, \infty\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`RR`	$\mathbb{R}$	Real numbers
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("466095"),
    Formula(LessEqual(Abs(Atan(x)), Abs(x))),
    Variables(x),
    Assumptions(Element(x, Union(RR, Set(Neg(Infinity), Infinity)))))

Topics using this entry

Inverse tangent

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