Branches History Index

◀ ▲ ▶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.

  1. Every Cauchy sequence converges, is called
  2. Every non-empty 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

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@Brenner

References

Adapted from CC BY-SA 3.0 Sources:

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