where f is any non-constant polynomial with real coefficients such that f(x) > 0 for all x > 0, then the concatenation a1a2a3... (with the an expressed in base b) is a normal sequence in base b, and is therefore disjunctive on {0, 1, ..., b-1}. E.g., using base-ten expressions, the sequences 818429218031851879211521610... (with f(x) = 2x3 - 5x2 + 11x ) 591215182124273034... (with f(x) = πx + e) are disjunctive on {0,1,2,3,4,5,6,7,8,9}. Rich numbers A rich number or disjunctive number is a real number whose expansion with respect to some base b is a disjunctive sequence over the alphabet {0,...,b−1}. Every normal number in base b is disjunctive but not conversely. The real number x is rich in base b if and only if the set { x bn mod 1} is dense in the unit interval. A number that is disjunctive to every base is called absolutely disjunctive or is said to be a lexicon. Every string in every alphabet occurs within a lexicon. A set is called "comeager" or "residual" if it contains the intersection of a countable family of open dense sets. The set of absolutely disjunctive reals is residual. It is conjectured that every real irrational algebraic number is absolutely disjunctive. Notes References Sequences and series