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 58 topics:

Greatest common divisor (in 36 entries)
Illustrations of Jacobi theta functions (in 19 entries)
Lambert W-function (in 17 entries)
Inverse tangent (in 16 entries)
Bounds and inequalities for the gamma function (in 15 entries)
Sinc function (in 13 entries)
Complex parts (in 13 entries)
Sine (in 12 entries)
Square roots (in 11 entries)
Chebyshev polynomials (in 11 entries)
Legendre polynomials (in 10 entries)
Bernoulli numbers and polynomials (in 8 entries)
Barnes G-function (in 8 entries)
Series representations of Carlson symmetric elliptic integrals (in 7 entries)
Natural logarithm (in 7 entries)
Dirichlet L-functions (in 7 entries)
Digamma function (in 7 entries)
Arithmetic-geometric mean (in 7 entries)
Riemann zeta function (in 6 entries)
Riemann hypothesis (in 6 entries)
Illustrations of Eisenstein series (in 6 entries)
Carlson symmetric elliptic integrals (in 6 entries)
Weierstrass elliptic functions (in 5 entries)
Series and product representations of Jacobi theta functions (in 5 entries)
Pi (in 5 entries)
General analytic functions (in 5 entries)
Exponential function (in 5 entries)
Bessel functions (in 5 entries)
Specific values of Carlson symmetric elliptic integrals (in 4 entries)
Powers (in 4 entries)
Gauss hypergeometric function (in 4 entries)
Gamma function (in 4 entries)
Confluent hypergeometric functions (in 4 entries)
Approximations of Jacobi theta functions (in 4 entries)
Modular lambda function (in 3 entries)
Jacobi theta functions (in 3 entries)
Factorials and binomial coefficients (in 3 entries)
Eisenstein series (in 3 entries)
Complex plane (in 3 entries)
Totient function (in 2 entries)
Partition function (in 2 entries)
Modular transformations (in 2 entries)
Modular j-invariant (in 2 entries)
Imaginary unit (in 2 entries)
Hurwitz zeta function (in 2 entries)
Halphen's constant (in 2 entries)
Gaussian quadrature (in 2 entries)
Dirichlet characters (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)
Stieltjes constants (in 1 entries)
Prime numbers (in 1 entries)
Keiper-Li coefficients (in 1 entries)
Fibonacci numbers (in 1 entries)
Euler's constant (in 1 entries)
Error functions (in 1 entries)

Entries using this symbol

The symbol Abs appears in 328 entries: