Noun
Dedekind cut (plural Dedekind cuts)
(mathematics) Any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.
In other words, the number line where every real number is defined as a Dedekind cut of rationals is a complete continuum without any further gaps. Source: Internet
It can be a simplification, in terms of notation if nothing more, to concentrate on one "half" — say, the lower one — and call any downward closed set A without greatest element a "Dedekind cut". Source: Internet
It is straightforward to show that a Dedekind cut among the real numbers is uniquely defined by the corresponding cut among the rational numbers. Source: Internet
The important purpose of the Dedekind cut is to work with number sets that are not complete. Source: Internet