Dedekind cuts can represent real numbers that are not rational, challenging the notion that they only produce a countable set. Each Dedekind cut is defined by a set of rational numbers, but these sets can converge to irrational numbers. For instance, a sequence of rational numbers can be derived from the decimal expansion of a real number, forming a cut that represents that real number. An example is the cut defined by the set of rationals whose squares are less than 2, which cannot be classified as a rational cut. Thus, Dedekind cuts encompass the entirety of the real line, including irrational numbers.
