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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)

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


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Bibliography (further reading)

[979] Reinhardt F., Soeder H.: “dtv-Atlas zur Mathematik”, Deutsche Taschenbuch Verlag, 1994, 10

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