Fungrim home page

Fungrim entry: 466095

∣atan⁡(x)∣≤∣x∣\left|\operatorname{atan}(x)\right| \le \left|x\right|
Assumptions:x∈R∪{−∞,∞}x \in \mathbb{R} \cup \left\{-\infty, \infty\right\}
TeX:
\left|\operatorname{atan}(x)\right| \le \left|x\right|

x \in \mathbb{R} \cup \left\{-\infty, \infty\right\}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
RRR\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

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

2021-03-15 19:12:00.328586 UTC