Dedekind cut
Dedekind cuts can be generalized from the rational numbers to any totally ordered set by defining a Dedekind cut as a partition of a totally ordered set into two non-empty parts "A" and "B", such that "A" is closed downwards (meaning that for all "a" in "A", "x" ≤ "a" implies that "x" is in "A" as well) and "B" is closed upwards, and "A" contains no greatest element. See also completeness (order theory).