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# Fungrim entry: 5e639e

Symbol: Sign $\operatorname{sgn}(z)$ Sign function
Domain Codomain
$z \in \mathbb{R}$ $\operatorname{sgn}(z) \in \left\{-1, 0, 1\right\}$
$z \in \mathbb{C} \setminus \left\{0\right\}$ $\operatorname{sgn}(z) \in \mathbb{T}$
$z \in \left\{\infty\right\}$ $\operatorname{sgn}(z) \in \left\{1\right\}$
$z \in \left\{-\infty\right\}$ $\operatorname{sgn}(z) \in \left\{-1\right\}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \implies \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
Sign$\operatorname{sgn}(z)$ Sign function
RR$\mathbb{R}$ Real numbers
CC$\mathbb{C}$ Complex numbers
UnitCircle$\mathbb{T}$ Unit circle
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("5e639e"),
SymbolDefinition(Sign, Sign(z), "Sign function"),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Sign(z), Set(-1, 0, 1))), Tuple(Element(z, SetMinus(CC, Set(0))), Element(Sign(z), UnitCircle)), Tuple(Element(z, Set(Infinity)), Element(Sign(z), Set(1))), Tuple(Element(z, Set(Neg(Infinity))), Element(Sign(z), Set(-1))))))

## Topics using this entry

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

2020-01-31 18:09:28.494564 UTC