# Canonical Cauchy sequences for real numbers

Rinat Kashaev

Rinat Kashaev

**12/10/20**Published in : arXiv:2010.05804

Based on continued fractions with subtractions, we identify the set of real numbers with the set of infinite integer sequences with all terms but the first one greater or equal to two. Each such sequence produces in a canonical way a unique strictly decreasing Cauchy sequence of rationals which converges to the corresponding real number. The correspondence is such that the standard order of real numbers is translated to the lexicographic order of sequences.