Axiom: Archimedean Axiom

Let \(x,y\) be two positive real numbers, i.e. \(x > 0\) and \(y > 0\). Then there exists a natural number \(n\) such that \(nx > y.\)

Actually, the axiom is applicable for any kind of ordered fields fulfilling the Archimedian principle.

Corollaries: 1 2 3 4 5

Definitions: 1
Proofs: 2 3 4
Theorems: 5


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983

Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück