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Fungrim entry: b7d740

Symbol: Arg arg(z)\arg(z) Complex argument
Domain Codomain
zRz \in \mathbb{R} arg(z){0,π}\arg(z) \in \left\{0, \pi\right\}
zCz \in \mathbb{C} arg(z)(π,π]\arg(z) \in \left(-\pi, \pi\right]
z{}z \in \left\{\infty\right\} arg(z){0}\arg(z) \in \left\{0\right\}
z{}z \in \left\{-\infty\right\} arg(z){π}\arg(z) \in \left\{\pi\right\}
Table data: (P,Q)\left(P, Q\right) such that (P)        (Q)\left(P\right) \;\implies\; \left(Q\right)
Fungrim symbol Notation Short description
Argarg(z)\arg(z) Complex argument
RRR\mathbb{R} Real numbers
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    SymbolDefinition(Arg, Arg(z), "Complex argument"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Arg(z), Set(0, Pi))), Tuple(Element(z, CC), Element(Arg(z), OpenClosedInterval(Neg(Pi), Pi))), Tuple(Element(z, Set(Infinity)), Element(Arg(z), Set(0))), Tuple(Element(z, Set(Neg(Infinity))), Element(Arg(z), Set(Pi))))))

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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