DECIMAL EXPANSIONS: THEIR UNIQUENESS AND INTERESTING PATTERNS
Journal Title: Journal of Ramanujan Society of Mathematics and Mathematical Sciences - Year 2017, Vol 6, Issue 1
Abstract
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.
Authors and Affiliations
Vishnu K Gurtu
Keywords
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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 irratio...