or real,n. any rational or irrational number. The reals, denoted R, are defined in terms of Cauchy sequences of, or Dedekind cuts on, the rationals. Technically, the rationals are not a subset of the reals but they are isomorphic to the subset of sequences that contain their supremum and are usually identified with those sequences. Whereas the rationals are denumerable, the reals are not; there are thus strictly more reals than there are integers or rationals. The reals are dense and form a compact connected set (a continuum); they are often referred to as the continuum. The sum of a real and an imaginary number is a complex number. See also Cantor's diagonal theorem, continuum hypothesis.