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

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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 $\backslash (T\; \backslash vDash\; \backslash phi\backslash )$ is true, then $\backslash (T\; \backslash vdash\; \backslash phi\backslash )$ 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 $\backslash (\backslash vDash\; F\backslash )$ [or even if $\backslash (\backslash aleph\_0\backslash )$-$\backslash (\backslash vDash\; F\backslash )$], then $\backslash (\backslash vdash\; F\backslash )$. If $\backslash (E\_1,\; .\; .\; ,\; E\_k\; \backslash vDash\; F\backslash )$ [or even if $\backslash (E\_1,\; .\; .\; ,\; E\_k\; \backslash \; \backslash aleph\_0\backslash )$-$\backslash (\backslash vDash\; F\backslash )$], then $\backslash (E\_1,\; .\; .\; ,\; E\_k\; \backslash vdash\; F\backslash )$.
(b) [...]

Synonyms

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

Antonyms

• incompleteness, unfinishedness; see also incompletion

Source: Wiktionary

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Com*plete"ness, n.

Definition: The state of being complete.

Source: Webster’s Unabridged Dictionary 1913 Edition

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