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 nonempty 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.

2.
Every bounded^{} monotonic sequence is convergent^{}.

3.
A sequence is convergent iff it is a Cauchy Sequence^{}.
Title  completeness principle 
Canonical name  CompletenessPrinciple 
Date of creation  20130322 12:23:06 
Last modified on  20130322 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 