different between completeness vs undefined

English

complete +? -ness

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 ? 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) [...]

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

un- +? defined

undefined (not comparable)

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.

(lacking a definition or value): indefinite, undefinable; see also Thesaurus:indistinct or Thesaurus:vague

Send