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Fungrim entry: 5e639e

Symbol: Sign sgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
Domain Codomain
zRz \in \mathbb{R} sgn ⁣(z){1,0,1}\operatorname{sgn}\!\left(z\right) \in \left\{-1, 0, 1\right\}
zC{0}z \in \mathbb{C} \setminus \left\{0\right\} sgn ⁣(z)T\operatorname{sgn}\!\left(z\right) \in \mathbb{T}
z{}z \in \left\{\infty\right\} sgn ⁣(z){1}\operatorname{sgn}\!\left(z\right) \in \left\{1\right\}
z{}z \in \left\{-\infty\right\} sgn ⁣(z){1}\operatorname{sgn}\!\left(z\right) \in \left\{-1\right\}
Table data: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
Signsgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
RRR\mathbb{R} Real numbers
CCC\mathbb{C} Complex numbers
UnitCircleT\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))))))

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

2019-09-19 20:12:49.583742 UTC