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Theorem vs Completeness - What's the difference?

theorem | completeness |

As nouns the difference between theorem and completeness

is that theorem is (mathematics) a mathematical statement of some importance that has been proven to be true minor theorems are often called propositions'' theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called ''lemmas while completeness is the state or condition of being complete.

As a verb theorem

is to formulate into a theorem.

theorem

English

Noun

(en noun)
  • (mathematics) A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions''. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called ''lemmas
  • (mathematics, colloquial, nonstandard) A mathematical statement that is expected to be true; as, (as which it was known long before it was proved in the 1990s.)
  • (logic) a syntactically correct expression that is deducible from the given axioms of a deductive system

    • Synonyms

    * (proven statement): lemma, proposition, statement * (unproven statement): conjecture * See also

    Holonyms

    * theory

    Derived terms

    * central limit theorem * Pythagorean theorem * binomial theorem * * intercept theorem

    Related terms

    * theoretical * theory

    Verb

    (en verb)
  • to formulate into a theorem

    • External links

    * * *

    completeness

    English

    (wikipedia completeness)

    Noun

    (-)
  • 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

    Antonyms

    * incompleteness