adj. 1. (of a metric space) having the property that every Cauchy sequence converges; for example, the real numbers are complete but the rationals are not, where the metric is the absolute difference between the numbers. 2. also called order complete or Dedekind complete. (of a partially ordered set) such that every subset has a supremum and infimum; for example, the reals are not complete but the interval [0, 1] is. 3. (of a graph) containing all possible edges between its vertices; thus the hexagon below is a complete graph, since every pair of vertices is joined by an edge.See also complete quadrilateral. 4. (of a logical theory) having the property that every (semantically) valid formula can be proved (syntactically) from the axioms. See also strong completeness. Compare consistent. 5. (of a sufficient statistic for a parameter θ) having the property that if the expected value of a function of the statistic is zero for all values of the parameter, then the function is identically zero. 6. (of a group) having a trivial center, and isomorphic to the group of its own automorphisms. 7. (of an orthonormal set) maximal. 8. (of a partially ordered set) another, more ambiguous, word for connected in the sense of a total order.