EXPANSIONS OF REAL NUMBERS IN NON-INTEGER BASES

- Journal title : Journal of the Korean Mathematical Society
- Volume 47, Issue 4, 2010, pp.861-877
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2010.47.4.861

Title & Authors

EXPANSIONS OF REAL NUMBERS IN NON-INTEGER BASES

Chunarom, Danita; Laohakosol, Vichian;

Chunarom, Danita; Laohakosol, Vichian;

Abstract

The works of Erds et al. about expansions of 1 with respect to a non-integer base q, referred to as q-expansions, are investigated to determine how far they continue to hold when the number 1 is replaced by a positive number x. It is found that most results about q-expansions for real numbers greater than or equal to 1 are in somewhat opposite direction to those for real numbers less than or equal to 1. The situation when a real number has a unique q-expansion, and when it has exactly two q-expansions are studied. The smallest base number q yielding a unique q-expansion is determined and a particular sequence is shown, in certain sense, to be the smallest sequence whose corresponding base number q yields exactly two q-expansions.

Keywords

expansions of numbers;non-integer bases;

Language

English

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