COMPLETENESS

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

completeness

(noun) the state of being complete and entire; having everything that is needed

Source: WordNet® 3.1


Etymology

Noun

completeness (usually uncountable, plural completenesses)

the state or condition of being complete

(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.

THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
(a) If \(\vDash F\) [or even if \(\aleph_0\)-\(\vDash F\)], then \(\vdash F\). If \(E_1, . . , E_k \vDash F\) [or even if \(E_1, . . , E_k \ \aleph_0\)-\(\vDash F\)], then \(E_1, . . , E_k \vdash F\).
(b) [...]

Synonyms

• (state of being complete): completion, fulfillment; see also completion

Antonyms

• incompleteness, unfinishedness; see also incompletion

Source: Wiktionary


Com*plete"ness, n.

Definition: The state of being complete.

Source: Webster’s Unabridged Dictionary 1913 Edition



RESET




Word of the Day

28 November 2024

SYNCRETISM

(noun) the fusion of originally different inflected forms (resulting in a reduction in the use of inflections)


coffee icon

Coffee Trivia

There are more than 50 countries that export coffee. They are near the equator, where the climate is conducive to producing coffee beans.

coffee icon