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Fungrim entry: 5e639e

Symbol: Sign sgn(z)\operatorname{sgn}(z) Sign function
Domain Codomain
zRz \in \mathbb{R} sgn(z){1,0,1}\operatorname{sgn}(z) \in \left\{-1, 0, 1\right\}
zC{0}z \in \mathbb{C} \setminus \left\{0\right\} sgn(z)T\operatorname{sgn}(z) \in \mathbb{T}
z{}z \in \left\{\infty\right\} sgn(z){1}\operatorname{sgn}(z) \in \left\{1\right\}
z{}z \in \left\{-\infty\right\} sgn(z){1}\operatorname{sgn}(z) \in \left\{-1\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
Signsgn(z)\operatorname{sgn}(z) 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:
    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.

2021-03-15 19:12:00.328586 UTC