# Fungrim entry: 3fe68f

Symbol: OpenInterval $\left(a, b\right)$ Open interval
OpenInterval(a, b) $\left(a, b\right)$ Represents $\left\{ x : x \in \mathbb{R} \cup \left\{-\infty, \infty\right\} \,\mathbin{\operatorname{and}}\, a < x < b \right\}$.
OpenInterval(0, 1) $\left(0, 1\right)$ Represents the open unit interval.
OpenInterval(1, 1) $\left(1, 1\right)$ Represents the empty set.
OpenInterval(Neg(Infinity), 0) $\left(-\infty, 0\right)$ Represents half the extended real line (excluding minus infinity and zero).
OpenInterval(1, -1) $\left(1, -1\right)$ Represents the empty set. Note: potentially confusing rendering.
Add(1, Mul(OpenInterval(0, 1), ConstI)) $1 + \left(0, 1\right) i$ Represents a set of points in the complex plane. OpenInterval(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(OpenInterval(1, 4), Mul(OpenInterval(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
OpenInterval$\left(a, b\right)$ Open interval
RR$\mathbb{R}$ Real numbers
Infinity$\infty$ Positive infinity
ConstI$i$ Imaginary unit
Source code for this entry:
Entry(ID("3fe68f"),
SymbolDefinition(OpenInterval, OpenInterval(a, b), "Open interval"),
CodeExample(OpenInterval(a, b), "Represents", Set(x, ForElement(x, Union(RR, Set(Neg(Infinity), Infinity))), Less(a, x, b)), "."),
CodeExample(OpenInterval(0, 1), "Represents the open unit interval."),
CodeExample(OpenInterval(1, 1), "Represents the empty set."),
CodeExample(OpenInterval(Neg(Infinity), 0), "Represents half the extended real line (excluding minus infinity and zero)."),
CodeExample(OpenInterval(1, -1), "Represents the empty set.", " Note: potentially confusing rendering."),
CodeExample(Add(1, Mul(OpenInterval(0, 1), ConstI)), "Represents a set of points in the complex plane. ", SourceForm(OpenInterval(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(OpenInterval(1, 4), Mul(OpenInterval(0, 1), ConstI)), "Represents a rectangle in the complex plane. "))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC