# 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.