◀ ▲ ▶Branches / Algebra / Definition: Complete Ordered Field
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 nonempty bounded subset has a supremum.
Example
Because of the completeness principle, the field of real numbers is a complete ordered field.
Mentioned in:
Definitions: 1
Proofs: 2
Theorems: 3
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References
Adapted from CC BYSA 3.0 Sources:
 Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück