Abbreviations & Definitions

To avoid redundancies I put some of the more often used abbreviations and the, mostly mathematical, definitions here.
(This blogging software does some weird things to the former definition list here, my…)

\mathbb{N}

The set of natural numbers according to Zermelo–Fraenkel (ZF) set theory:
Define 0 = \{\} and n+1=n\cup\{n\} to construct finite sets whose cardinalities build the set of the naturals numbers \mathbb{N}.
tl;dr: \mathbb{N} = \{0,1,2,3,\cdots\}

\mathbb{N}^+

\mathbb{N}^+ = \mathbb{N}\setminus\{0\}

\mathbb{Z}

\mathbb{Z} = \{n,-n|n\in\mathbb{N}\}

\mathbb{Z}^*

\mathbb{Z}^* = \mathbb{N}

\mathbb{Z}^*

\mathbb{Z}^* = \mathbb{N}^+

\mathbb{Z}/n

\mathbb{Z}/n is the set of integers modulo n

\mathbb{P}

\mathbb{P} is the set of primes

\infty

\infty is not a number. Nevertheless it gets used here in limits like \lim_{x\to 0}\tfrac{1}{x}=\infty or \sum_{n=1}\tfrac{1}{n}. It is invisible in the latter example. Twice.

{}^*\mathbb{N}\setminus\mathbb{N}

is the set of infinite integers. Not used here.

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