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Definition: Complete Ordered Field
An ordered field, in which one of the following (equivalent) rules is fulfilled is called a complete ordered field.
- Every Cauchy sequence converges, is called
- Every non-empty bounded subset has a supremum.
Because of the completeness principle, the field of real numbers is a complete ordered field.
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Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück