# completeness axiom

## English[edit]

### Noun[edit]

**completeness axiom** (*plural* **completeness axioms**)

- (mathematics) The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).