Associations to the word «Completeness»

COMPLETENESS, noun. The state or condition of being complete

COMPLETENESS, noun. (logic) The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever \(T \vDash \phi\) is true, then \(T \vdash \phi\) must also be true, for any wff φ of logic L.

COMPLETENESS AXIOM, noun. (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).

COMPLETENESS, noun. The state of being complete and entire; having everything that is needed.

COMPLETENESS, noun. (logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system.