On using bounded continued fractions to represent reals

Abstract

The continued fraction representation of an arbitrary real will have partial quotients that exceed any specified upper limit, making their representation on a computer difficult. However, any real can be represented as the sum of two continued fractions with an upper bound on their partial quotients. Here, algorithms are developed to actually find these bounded continued fractions for arbitrary reals and rationals. Whereas the real form is not competitive with the standard representation of reals on a computer, the rational representation shows promise. We also conjecture that there are an infinite number of representations available for any real.