# 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.