Definition: Definition of Irrational Numbers

The irrational numbers are the set difference $\mathbb R\setminus\mathbb Q$ between the set of real numbers $\mathbb R$ and the set of rational numbers $\mathbb Q$.

Obviously, the set is not empty, since $\sqrt 2\in\mathbb R\setminus\mathbb Q$ due to discovery of Ancient Greeks.

Chapters: 1
Corollaries: 2
Definitions: 3
Motivations: 4
Proofs: 5
Propositions: 6


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
  2. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013