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Completeness vs Undefined - What's the difference?

completeness | undefined |

As a noun completeness

is the state or condition of being complete.

As an adjective undefined is

lacking a definition or value.

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

    undefined

    English

    Adjective

    (wikipedia undefined) (-)
  • Lacking a definition or value.
  • (mathematics, computing) That does not have a meaning and is thus not assigned an interpretation.
    • The result of division by zero is undefined .

    Antonyms

    * defined