Fungrim entry: 12d5ab

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 entry

Numbers and infinities