Fungrim symbol: OpenClosedInterval

Symbol: OpenClosedInterval —

\left(a, b\right]

— Open-closed interval

►OpenClosedInterval(a, b) —

\left(a, b\right]

— Represents

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

►OpenClosedInterval(0, 1) —

\left(0, 1\right]

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

►OpenClosedInterval(1, 1) —

\left(1, 1\right]

— Represents the empty set.

►OpenClosedInterval(Neg(Infinity), 0) —

\left(-\infty, 0\right]

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

►OpenClosedInterval(1, -1) —

\left(1, -1\right]

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

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

1 + \left(0, 1\right] i

— Represents a set of points in the complex plane. OpenClosedInterval(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(OpenClosedInterval(1, 4), Mul(OpenClosedInterval(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
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`RR`	$\mathbb{R}$	Real numbers
`Infinity`	$\infty$	Positive infinity
`ConstI`	$i$	Imaginary unit

Source code for this entry:

Entry(ID("ed302a"),
    SymbolDefinition(OpenClosedInterval, OpenClosedInterval(a, b), "Open-closed interval"),
    CodeExample(OpenClosedInterval(a, b), "Represents", Set(x, ForElement(x, Union(RR, Set(Neg(Infinity), Infinity))), And(Less(a, x), LessEqual(x, b))), "."),
    CodeExample(OpenClosedInterval(0, 1), "Represents the unit interval (excluding 0, including 1)."),
    CodeExample(OpenClosedInterval(1, 1), "Represents the empty set."),
    CodeExample(OpenClosedInterval(Neg(Infinity), 0), "Represents half the extended real line (excluding minus infinity, including zero)."),
    CodeExample(OpenClosedInterval(1, -1), "Represents the empty set.", " Note: potentially confusing rendering."),
    CodeExample(Add(1, Mul(OpenClosedInterval(0, 1), ConstI)), "Represents a set of points in the complex plane. ", SourceForm(OpenClosedInterval(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(OpenClosedInterval(1, 4), Mul(OpenClosedInterval(0, 1), ConstI)), "Represents a rectangle in the complex plane. "))

Topics using this symbol

The symbol OpenClosedInterval appears in 24 topics:

Carlson symmetric elliptic integrals (in 19 entries)
Series representations of Carlson symmetric elliptic integrals (in 16 entries)
Inverse tangent (in 15 entries)
Square roots (in 11 entries)
Lambert W-function (in 11 entries)
Arithmetic-geometric mean (in 10 entries)
Natural logarithm (in 7 entries)
Coulomb wave functions (in 7 entries)
Barnes G-function (in 7 entries)
Specific values of Carlson symmetric elliptic integrals (in 4 entries)
Gamma function (in 4 entries)
Sinc function (in 2 entries)
Gauss hypergeometric function (in 2 entries)
Exponential function (in 2 entries)
Digamma function (in 2 entries)
Chebyshev polynomials (in 2 entries)
Riemann zeta function (in 1 entries)
Numbers and infinities (in 1 entries)
Modular lambda function (in 1 entries)
Legendre elliptic integrals (in 1 entries)
Hurwitz zeta function (in 1 entries)
Halphen's constant (in 1 entries)
Dirichlet L-functions (in 1 entries)
Complex parts (in 1 entries)

Entries using this symbol

The symbol OpenClosedInterval appears in 127 entries: