In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression..

All Cauchy sequences are convergent.

In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine Extract of page 209 Extract of page 30 (devised by English mathematician and computer scientist Alan Turing).

Completeness is a property of the real numbers that, intuitively, implies that there are no "gaps" (in Dedekind's terminology) or "missing points" in the real number line.