denumerable set[də′nüm·rə·bəl ′set]
(or countably infinite set), an infinite set whose elements can be indexed by the natural numbers—that is, a one-to-one correspondence can be established between the set of all natural numbers. As G. Cantor demonstrated, the set of all rational numbers and even the set of all algebraic numbers are denumerable, but the set of all real numbers is nondenumerable. Every infinite set contains a denumerable subset. The union of a finite or denumerable set of denumerable sets is also a denumerable set.