# Fungrim entry: b7d740

Symbol: Arg $\arg\!\left(z\right)$ Complex argument
Domain Codomain
$z \in \mathbb{R}$ $\arg\!\left(z\right) \in \left\{0, \pi\right\}$
$z \in \mathbb{C}$ $\arg\!\left(z\right) \in \left(-\pi, \pi\right]$
$z \in \left\{\infty\right\}$ $\arg\!\left(z\right) \in \left\{0\right\}$
$z \in \left\{-\infty\right\}$ $\arg\!\left(z\right) \in \left\{\pi\right\}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \implies \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
Arg$\arg\!\left(z\right)$ Complex argument
RR$\mathbb{R}$ Real numbers
ConstPi$\pi$ The constant pi (3.14...)
CC$\mathbb{C}$ Complex numbers
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("b7d740"),
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, ConstPi))), Tuple(Element(z, CC), Element(Arg(z), OpenClosedInterval(Neg(ConstPi), ConstPi))), Tuple(Element(z, Set(Infinity)), Element(Arg(z), Set(0))), Tuple(Element(z, Set(Neg(Infinity))), Element(Arg(z), Set(ConstPi))))))

## Topics using this entry

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

2019-09-15 13:58:57.282983 UTC