completeness

English

Alternative forms

• completenesse (obsolete)

Etymology

Etymology tree

Middle English compleet

English complete

Proto-Germanic *-in-

Proto-Indo-European *-h₂

Proto-Indo-European *-éh₂

Proto-Indo-European *-yéti

Proto-Indo-European *-eh₂yéti

Proto-Indo-European *-h₂ti

Proto-Germanic *-ōną

Proto-Germanic *-inōną

Proto-Indo-European *-dyé-der.

Proto-Germanic *-atjaną

Proto-Indo-European *-tus

Proto-Germanic *-þuz

Proto-Germanic *-assuz

Proto-Germanic *-inassuz

Proto-West Germanic *-nassī

Old English -nes

Middle English -nesse

English -ness

English completeness

From complete + -ness.

Noun

completeness (usually uncountable, plural completenesses)

1. The state or condition of being complete.
2. (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 $T\models \varphi$ is true, then $T⊢\varphi$ must also be true, for any wff φ of logic L.
   • 2002, Stephen Cole Kleene, Mathematical Logic, Mineola, New York: Dover Publications, →ISBN, page 314:

     THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
     (a) If $\models F$ [or even if ${\mathrm{\aleph }}_0$-$\models F$], then $⊢F$. If $E_1,\mathrm{...},E_k\models F$ [or even if $E_1,\mathrm{...},E_k{\mathrm{\aleph }}_0$-$\models F$], then $E_1,\mathrm{...},E_k⊢F$.
     (b) […]

Synonyms

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

Antonyms

• incompleteness, unfinishedness; see also Thesaurus:incompletion

Derived terms

• completeness axiom

Related terms

• co-NP-completeness

Translations

state or condition of being complete

• Bulgarian: ця́лостност (bg) (cjálostnost), завърше́ност (bg) (zavăršénost)
• Catalan: completesa (ca) f, completud f, completitud f
• Chinese:

  Mandarin: 完整性 (zh) (wánzhěngxìng)

• Czech: úplnost f
• Esperanto: tuteco
• Finnish: täydellisyys (fi), valmius (fi)
• French: complétude (fr) f
• German: Vollständigkeit (de) f
• Greek:

  Ancient Greek: ἐντέλεια f (entéleia)

• Hebrew: שלמות f (shlemut)
• Hindi: पूर्णता (hi) f (pūrṇatā), संपूर्णता f (sampūrṇatā)
• Indonesian: kelengkapan (id)
• Irish: foirfeacht f
• Italian: completezza (it) f
• Polish: całkowitość (pl) f, kompletność (pl) f, zupełność (pl) f, pełnia (pl) f
• Portuguese: completidão f, completude (pt) f
• Russian: полнота́ (ru) f (polnotá), завершёность f (zaveršónostʹ), зако́нченнность f (zakónčennnostʹ), це́лостность (ru) f (célostnostʹ)
• Spanish: completitud (es) f, completud (es) f, completez (es) f, plenitud (es) f
• Swedish: fullständighet (sv) c
• Turkish: bütünlük (tr)