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Numbers and infinities

Table of contents: Numbers - Infinities - Ranges and intervals

Numbers

Standard number domains

298e9e
Symbol: ZZ Z\mathbb{Z} Integers
7be5dc
Symbol: QQ Q\mathbb{Q} Rational numbers
bfe358
Symbol: RR R\mathbb{R} Real numbers
0deea6
Symbol: CC C\mathbb{C} Complex numbers
4fd123
ZQRC\mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}

Rational numbers

c01d22
Q={pq:pZandqZ{0}}\mathbb{Q} = \left\{ \frac{p}{q} : p \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, q \in \mathbb{Z} \setminus \left\{0\right\} \right\}
81c491
2Q\sqrt{2} \notin \mathbb{Q}
0c838a
πQ\pi \notin \mathbb{Q}

Complex numbers

Related topics: Imaginary unit, Complex plane
88ad6f
iCi \in \mathbb{C}
72cef9
i=1i = \sqrt{-1}
a08fb9
iRi \notin \mathbb{R}
77ef0c
C={x+yi:xRandyR}\mathbb{C} = \left\{ x + y i : x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \right\}

Algebraic numbers

be9c83
Symbol: AlgebraicNumbers Q\overline{\mathbb{Q}} Algebraic numbers
aa6b07
Q={z:zCandthere exists f with fZ[x]{0}andf(z)=0}\overline{\mathbb{Q}} = \left\{ z : z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \text{there exists } f \text{ with } f \in \mathbb{Z}[x] \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, f(z) = 0 \right\}
e5a04c
ZQQC\mathbb{Z} \subset \mathbb{Q} \subset \overline{\mathbb{Q}} \subset \mathbb{C}
24c179
2Q\sqrt{2} \in \overline{\mathbb{Q}}
cd8a07
iQi \in \overline{\mathbb{Q}}
155575
πQ\pi \notin \overline{\mathbb{Q}}

Infinities

b738b1
Symbol: Infinity \infty Positive infinity
486ab2
Symbol: UnsignedInfinity ~{\tilde \infty} Unsigned infinity

Ranges and intervals

03fbae
Symbol: ZZGreaterEqual Zn\mathbb{Z}_{\ge n} Integers greater than or equal to n
2a52af
Symbol: ZZLessEqual Zn\mathbb{Z}_{\le n} Integers less than or equal to n
00b82b
Symbol: Range {a,a+1,,b}\{a, a + 1, \ldots, b\} Integers between given endpoints
12d5ab
Symbol: ClosedInterval [a,b]\left[a, b\right] Closed interval
3fe68f
Symbol: OpenInterval (a,b)\left(a, b\right) Open interval
b2162a
Symbol: ClosedOpenInterval [a,b)\left[a, b\right) Closed-open interval
ed302a
Symbol: OpenClosedInterval (a,b]\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.

2019-11-11 15:50:15.016492 UTC