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 step-by-step manner by certain structural properties to allow such operations.

Theoretical minimum (in a nutshell)

• You should be acquainted with set theory, especially
  • set operations,
  • functions,
  • order relations, and
  • countability.
• For a deeper understanding, you should know some basic facts about
  • algebraic structures, including groups, integral domain, and fields.
  • The topological concept of a metric space.

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.

| | | | created: 2014-02-20 23:39:12 | modified: 2019-01-20 20:34:50 | by: bookofproofs | references: [979]

1.Natural Numbers

2.Integers

3.Rational Numbers

4.Irrational Numbers

5.Real Numbers

6.Complex Numbers

7.Explanation: Comparison Between the Number Systems

8.Solving Strategies and Sample Solutions Related to Arithmetics