Fungrim symbol: ClosedInterval

Symbol: ClosedInterval —

\left[a, b\right]

— Closed interval

►ClosedInterval(a, b) —

\left[a, b\right]

— Represents

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

►ClosedInterval(0, 1) —

\left[0, 1\right]

— Represents the closed unit interval.

►ClosedInterval(1, 1) —

\left[1, 1\right]

— Represents the singleton set {1}.

►ClosedInterval(Neg(Infinity), 0) —

\left[-\infty, 0\right]

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

►ClosedInterval(1, -1) —

\left[1, -1\right]

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

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

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

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

Source code for this entry:

Entry(ID("12d5ab"),
    SymbolDefinition(ClosedInterval, ClosedInterval(a, b), "Closed interval"),
    CodeExample(ClosedInterval(a, b), "Represents", Set(x, ForElement(x, Union(RR, Set(Neg(Infinity), Infinity))), LessEqual(a, x, b)), "."),
    CodeExample(ClosedInterval(0, 1), "Represents the closed unit interval."),
    CodeExample(ClosedInterval(1, 1), "Represents the singleton set", Set(1), "."),
    CodeExample(ClosedInterval(Neg(Infinity), 0), "Represents half the extended real line (including minus infinity and zero)."),
    CodeExample(ClosedInterval(1, -1), "Represents the empty set.", " Note: potentially confusing rendering."),
    CodeExample(Add(1, Mul(ClosedInterval(0, 1), ConstI)), "Represents a set of points in the complex plane. ", SourceForm(ClosedInterval(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(ClosedInterval(1, 4), Mul(ClosedInterval(0, 1), ConstI)), "Represents a rectangle in the complex plane. "))

Topics using this symbol

The symbol ClosedInterval appears in 32 topics:

Illustrations of Jacobi theta functions (in 19 entries)
Legendre elliptic integrals (in 10 entries)
Jacobi theta functions (in 6 entries)
Illustrations of Eisenstein series (in 6 entries)
Chebyshev polynomials (in 6 entries)
Carlson symmetric elliptic integrals (in 5 entries)
Sine (in 4 entries)
Integrals of Jacobi theta functions (in 4 entries)
Gamma function (in 4 entries)
Weierstrass elliptic functions (in 3 entries)
Hurwitz zeta function (in 3 entries)
Barnes G-function (in 3 entries)
Sinc function (in 2 entries)
Modular lambda function (in 2 entries)
Legendre polynomials (in 2 entries)
Lambert W-function (in 2 entries)
Inverse tangent (in 2 entries)
General analytic functions (in 2 entries)
Exponential function (in 2 entries)
Eisenstein series (in 2 entries)
Digamma function (in 2 entries)
Beta function (in 2 entries)
Arithmetic-geometric mean (in 2 entries)
Airy functions (in 2 entries)
Square roots (in 1 entries)
Riemann zeta function (in 1 entries)
Pi (in 1 entries)
Numbers and infinities (in 1 entries)
Natural logarithm (in 1 entries)
Modular j-invariant (in 1 entries)
Error functions (in 1 entries)
Bernoulli numbers and polynomials (in 1 entries)

Entries using this symbol

The symbol ClosedInterval appears in 98 entries: