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Fungrim entry: 920cc8

Symbol: Abs z\left|z\right| Absolute value
Domain Codomain
zRz \in \mathbb{R} z[0,)\left|z\right| \in \left[0, \infty\right)
zCz \in \mathbb{C} z[0,)\left|z\right| \in \left[0, \infty\right)
z{,,~}z \in \left\{\infty, -\infty, {\tilde \infty}\right\} z{}\left|z\right| \in \left\{\infty\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
Absz\left|z\right| Absolute value
RRR\mathbb{R} Real numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
UnsignedInfinity~{\tilde \infty} Unsigned infinity
Source code for this entry:
    SymbolDefinition(Abs, Abs(z), "Absolute value"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Abs(z), ClosedOpenInterval(0, Infinity))), Tuple(Element(z, CC), Element(Abs(z), ClosedOpenInterval(0, Infinity))), Tuple(Element(z, Set(Infinity, Neg(Infinity), UnsignedInfinity)), Element(Abs(z), Set(Infinity))))))

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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