Branch: Number Systems and Arithmetics
Number systems and arithmetics is a branch of mathematics dealing with a formal clarification of what numbers are and in which domains numbers allow arithmetical operations like addition, subtraction, multiplication, and division. It also describes how these domains can be extended in a stepbystep manner by certain structural properties to allow such operations.
Theoretical minimum (in a nutshell)
 You should be acquainted with set theory, especially
 For a deeper understanding, you should know some basic facts about
Concepts you will learn in this part of BookofProofs
 What are natural numbers, and how the can be defined using the axiomatic method?
 What are integers, how they can be defined using natural numbers and how they extend the calculating possibilities of natural numbers?
 What are rational numbers, how they can be defined using integers and how they extend the calculating possibilities of integers?
 What are real numbers, how they can be defined using rational numbers and how they extend the calculating possibilities of rational numbers?
 What are complex numbers, how they can be defined using real numbers and how they extend the calculating possibilities of real numbers?
 What are quaternions, how they can be defined using complex numbers and how they extend the calculating possibilities of complex numbers?
 What are the differences of the above domains, covering their algebraic, topological, and order properties.
Table of Contents
Explanations: 1
 Part: Natural Numbers
 Part: Integers
 Part: Rational Numbers
 Part: Irrational Numbers
 Part: Real Numbers
 Part: Complex Numbers
 Part: Solving Strategies and Sample Solutions Related to Arithmetics
Mentioned in:
Branches: 1
Chapters: 2
Definitions: 3 4
Explanations: 5 6
Motivations: 7 8
Parts: 9 10 11 12
Topics: 13
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Reinhardt F., Soeder H.: "dtvAtlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition