completeness axiom
completeness axiom · completeness axioms
The following axiom: for any subset of the given ordered field, if there is any upper…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).
Meaning
1 sensesThe 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).
Forms
plural: completeness axioms| Singular | completeness axiom |
|---|---|
| Plural | completeness axioms |
regular