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.
-
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 | 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 |