Fungrim entry: ed302a

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 entry

Numbers and infinities