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Fungrim entry: 4d2168

∣atan⁡ ⁣(x+y)−atan⁡ ⁣(x)∣<π\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}\!\left(x\right)\right| \lt \pi
Assumptions:x∈R and⁡ y∈Rx \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R}
TeX:
\left|\operatorname{atan}\!\left(x + y\right) - \operatorname{atan}\!\left(x\right)\right| \lt \pi

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Atanatan⁡ ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
ConstPiπ\pi The constant pi (3.14...)
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("4d2168"),
    Formula(Less(Abs(Sub(Atan(Add(x, y)), Atan(x))), ConstPi)),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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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