Fungrim symbol: Abs

Symbol: Abs —

\left|z\right|

— Absolute value

Domain	Codomain
$z \in \mathbb{R}$	$\left\|z\right\| \in \left[0, \infty\right)$
$z \in \mathbb{C}$	$\left\|z\right\| \in \left[0, \infty\right)$
$z \in \left\{\infty, -\infty, {\tilde \infty}\right\}$	$\left\|z\right\| \in \left\{\infty\right\}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \implies \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`RR`	$\mathbb{R}$	Real numbers
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity

Source code for this entry:

Entry(ID("920cc8"),
    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))))))

Topics using this symbol

The symbol Abs appears in 34 topics:

Greatest common divisor (in 36 entries)
Lambert W-function (in 17 entries)
Inverse tangent (in 15 entries)
Bounds and inequalities for the gamma function (in 15 entries)
Complex parts (in 13 entries)
Sine (in 12 entries)
Square roots (in 11 entries)
Legendre polynomials (in 10 entries)
Chebyshev polynomials (in 10 entries)
Bernoulli numbers and polynomials (in 8 entries)
Riemann zeta function (in 6 entries)
Natural logarithm (in 6 entries)
General analytic functions (in 5 entries)
Exponential function (in 5 entries)
Bessel functions (in 5 entries)
Powers (in 4 entries)
Pi (in 4 entries)
Gauss hypergeometric function (in 4 entries)
Gamma function (in 4 entries)
Confluent hypergeometric functions (in 4 entries)
Weierstrass elliptic functions (in 3 entries)
Factorials and binomial coefficients (in 3 entries)
Complex plane (in 3 entries)
Partition function (in 2 entries)
Modular transformations (in 2 entries)
Modular j-invariant (in 2 entries)
Gaussian quadrature (in 2 entries)
Dedekind eta function (in 2 entries)
Airy functions (in 2 entries)
Zeros of the Riemann zeta function (in 1 entries)
Stirling numbers (in 1 entries)
Prime numbers (in 1 entries)
Euler's constant (in 1 entries)
Error functions (in 1 entries)

Entries using this symbol

The symbol Abs appears in 215 entries: