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Fungrim entry: 5d6f74

∣atan⁡(x)∣≤π2\left|\operatorname{atan}(x)\right| \le \frac{\pi}{2}
Assumptions:x∈R∪{−∞,∞}x \in \mathbb{R} \cup \left\{-\infty, \infty\right\}
TeX:
\left|\operatorname{atan}(x)\right| \le \frac{\pi}{2}

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
Piπ\pi The constant pi (3.14...)
RRR\mathbb{R} Real numbers
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("5d6f74"),
    Formula(LessEqual(Abs(Atan(x)), Div(Pi, 2))),
    Variables(x),
    Assumptions(Element(x, Union(RR, Set(Neg(Infinity), Infinity)))))

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2021-03-15 19:12:00.328586 UTC