Mathematics-Online course: Preparatory Course Mathematics-Basics-Sets-Sets of Numbers

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	Mathematics-Online course: Preparatory Course Mathematics - Basics - Sets
	Sets of Numbers

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The following sets are standardly denoted by the respective symbols:

natural numbers: $\mathbb{N} = \{1,2,\ldots\}$
integers: $\mathbb{Z} = \{\ldots,-1,0,1,\ldots\}$
rational numbers: $\mathbb{Q} = \{p/q:\ p\in\mathbb{Z},\, q\in\mathbb{N},\,\operatorname{gcd}(p,q)=1\}$
real numbers: $\mathbb{R} = \{x:\ x=\lim_{n\to\infty} q_n,\, q_n\in\mathbb{Q}\}$
complex numbers: $\mathbb{C} = \{x+\mathrm{i}y:\ x,y\in\mathbb{R},\, \mathrm{i}^2=-1\}$

The following notations are also commonly used: $\mathbb{N}_0=\mathbb{N}\cup\{0\}$ and $\mathbb{R}^+ = \{x\in\mathbb{R}:\ x > 0\}$ as well as $\mathbb{Z}^-$ , $\mathbb{Z}^-_0$ , $\mathbb{Q}^+$ , $\mathbb{Q}^+_0$ , $\mathbb{Q}^-$ , $\mathbb{Q}^-_0$ $\mathbb{R}^+_0$ , $\mathbb{R}^-$ , $\mathbb{R}^-_0$ , respectively.

(Authors: Höllig/Abele)

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automatically generated 1/9/2017