# completeness principle

The completeness principle is a property of the real numbers, and is one of the foundations of real analysis. The most common formulation of this principle is that every non-empty set which is bounded from above has a supremum.

This statement can be reformulated in several ways. Each of the following statements is to the above definition of the completeness principle:

1. 1.

The limit of every infinite decimal sequence is a real number.

2. 2.
3. 3.

A sequence is convergent iff it is a Cauchy Sequence.

 Title completeness principle Canonical name CompletenessPrinciple Date of creation 2013-03-22 12:23:06 Last modified on 2013-03-22 12:23:06 Owner mathcam (2727) Last modified by mathcam (2727) Numerical id 12 Author mathcam (2727) Entry type Axiom Classification msc 54E50 Synonym completeness Axiom Synonym completeness principle Synonym least upper bound property Related topic ConvergentSequence Related topic ExistenceOfSquareRootsOfNonNegativeRealNumbers Related topic BoundedComplete