◀ ▲ ▶Branches / Number-systems-arithmetics / Proposition: Algebraic Structure of Real Numbers Together with Addition and Multiplication

Proposition: Algebraic Structure of Real Numbers Together with Addition and Multiplication

The set of real numbers \(\mathbb R\), together with the specific addition operation "\(+\)", and the specific multiplication operation "\(\cdot\)", forms the algebraic structure \((\mathbb R, + , \cdot)\) of a field.

Notes

Real numbers have an even more interesting structures than just being a field. In particular, they fulfill the Archimedean axiom and the completeness property. However, these additional features require a more detailed study of the properties of real numbers.

Table of Contents

Proofs: 1 2

Mentioned in:

Chapters: 1
Definitions: 2 3 4
Examples: 5
Explanations: 6
Parts: 7 8
Proofs: 9 10 11 12 13 14
Propositions: 15 16 17 18 19 20 21
Theorems: 22

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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