Fungrim symbol: ClosedOpenInterval

Symbol: ClosedOpenInterval —

\left[a, b\right)

— Closed-open interval

►ClosedOpenInterval(a, b) —

\left[a, b\right)

— Represents

\left\{ x : x \in \mathbb{R} \cup \left\{-\infty, \infty\right\} \,\mathbin{\operatorname{and}}\, a \le x \;\mathbin{\operatorname{and}}\; x < b \right\}

►ClosedOpenInterval(0, 1) —

\left[0, 1\right)

— Represents the unit interval (including 0, excluding 1).

►ClosedOpenInterval(1, 1) —

\left[1, 1\right)

— Represents the empty set.

►ClosedOpenInterval(Neg(Infinity), 0) —

\left[-\infty, 0\right)

— Represents half the extended real line (including minus infinity, excluding zero).

►ClosedOpenInterval(1, -1) —

\left[1, -1\right)

— Represents the empty set. Note: potentially confusing rendering.

►Add(1, Mul(ClosedOpenInterval(0, 1), ConstI)) —

1 + \left[0, 1\right) i

— Represents a set of points in the complex plane. ClosedOpenInterval(a, b) should only be used with extended real number

a

and

b

as endpoints, but line segments in the complex plane can be constructed by applying arithmetic operations to a set of real numbers (acting pointwise).

►Add(ClosedOpenInterval(1, 4), Mul(ClosedOpenInterval(0, 1), ConstI)) —

\left[1, 4\right) + \left[0, 1\right) i

— Represents a rectangle in the complex plane.

Definitions:

Fungrim symbol	Notation	Short description
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`RR`	$\mathbb{R}$	Real numbers
`Infinity`	$\infty$	Positive infinity
`ConstI`	$i$	Imaginary unit

Source code for this entry:

Entry(ID("b2162a"),
    SymbolDefinition(ClosedOpenInterval, ClosedOpenInterval(a, b), "Closed-open interval"),
    CodeExample(ClosedOpenInterval(a, b), "Represents", Set(x, ForElement(x, Union(RR, Set(Neg(Infinity), Infinity))), And(LessEqual(a, x), Less(x, b))), "."),
    CodeExample(ClosedOpenInterval(0, 1), "Represents the unit interval (including 0, excluding 1)."),
    CodeExample(ClosedOpenInterval(1, 1), "Represents the empty set."),
    CodeExample(ClosedOpenInterval(Neg(Infinity), 0), "Represents half the extended real line (including minus infinity, excluding zero)."),
    CodeExample(ClosedOpenInterval(1, -1), "Represents the empty set.", " Note: potentially confusing rendering."),
    CodeExample(Add(1, Mul(ClosedOpenInterval(0, 1), ConstI)), "Represents a set of points in the complex plane. ", SourceForm(ClosedOpenInterval(a, b)), "should only be used with extended real number", a, "and", b, "as endpoints, but line segments in the complex plane can be constructed by applying arithmetic operations to a set of real numbers (acting pointwise)."),
    CodeExample(Add(ClosedOpenInterval(1, 4), Mul(ClosedOpenInterval(0, 1), ConstI)), "Represents a rectangle in the complex plane. "))

Topics using this symbol

The symbol ClosedOpenInterval appears in 22 topics:

Inverse tangent (in 21 entries)
Carlson symmetric elliptic integrals (in 14 entries)
Square roots (in 9 entries)
Gauss hypergeometric function (in 9 entries)
Specific values of Carlson symmetric elliptic integrals (in 8 entries)
Legendre elliptic integrals (in 6 entries)
Lambert W-function (in 5 entries)
Bessel functions (in 5 entries)
Chebyshev polynomials (in 3 entries)
Bounds and inequalities for the gamma function (in 3 entries)
Arithmetic-geometric mean (in 3 entries)
Eisenstein series (in 2 entries)
Complex plane (in 2 entries)
Riemann hypothesis (in 1 entries)
Numbers and infinities (in 1 entries)
Natural logarithm (in 1 entries)
Modular transformations (in 1 entries)
Modular lambda function (in 1 entries)
Keiper-Li coefficients (in 1 entries)
Gamma function (in 1 entries)
Complex parts (in 1 entries)
Barnes G-function (in 1 entries)

Entries using this symbol

The symbol ClosedOpenInterval appears in 98 entries: