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 equivalent to the above definition of the completeness principle:

1. The limit of every infinite decimal sequence is a real number.
2. Every bounded monotonic sequence is convergent.
3. A sequence is convergent iff it is a Cauchy Sequence.