# Numbers and infinities

## Numbers

Symbol: ZZ $\mathbb{Z}$ Integers
Symbol: QQ $\mathbb{Q}$ Rational numbers
Symbol: RR $\mathbb{R}$ Real numbers
Symbol: CC $\mathbb{C}$ Complex numbers
Symbol: ConstI $i$ Imaginary unit
$\mathbb{Q} = \left\{ \frac{p}{q} : p \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, q \in \mathbb{Z} \setminus \left\{0\right\} \right\}$
${i}^{2} = -1$
$\mathbb{C} = \left\{ x + y i : x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \right\}$
$\mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$

## Algebraic numbers

Symbol: AlgebraicNumbers $\overline{\mathbb{Q}}$ Algebraic numbers
$\mathbb{Z} \subset \mathbb{Q} \subset \overline{\mathbb{Q}} \subset \mathbb{C}$

## Infinities

Symbol: Infinity $\infty$ Positive infinity
Symbol: UnsignedInfinity ${\tilde \infty}$ Unsigned infinity

## Ranges and intervals

Symbol: ZZGreaterEqual $\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Symbol: ZZLessEqual $\mathbb{Z}_{\le n}$ Integers less than or equal to n
Symbol: ZZBetween $\{a, a + 1, \ldots b\}$ Integers between a and b inclusive
Symbol: ClosedInterval $\left[a, b\right]$ Closed interval
Symbol: OpenInterval $\left(a, b\right)$ Open interval
Symbol: ClosedOpenInterval $\left[a, b\right)$ Closed-open interval
Symbol: OpenClosedInterval $\left(a, b\right]$ Open-closed interval

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

2019-06-18 07:49:59.356594 UTC