DECIMAL EXPANSIONS: THEIR UNIQUENESS AND INTERESTING PATTERNS

An expression of the form o.abcd... written by arbitrarily picking up a, b, c, d ... from among 0 to 9, cannot be taken to represent the decimal expansion of a real number. In fact, the decimal expansion of every irrational number is unique in itself whereas those of rational numbers (fractions) follow some interesting patterns. These results are of far-reaching consequences in the context of Cantor's second proof (1878) about the uncountability of real numbers.