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The b-parts of real numbers and the generalized division algorithm were considered and discussed in . Also some of their algebraic properties have been studied in . In this paper we continue it and introduce a unique finite representation of real numbers to the base of an arbitrary real number b ≠ 0, ± 1 (namely finite b-representation), by using them. Finally we prove a necessary and sufficient conditions for the finite b-representation to be digital.
- b-integer part
- b-decimal part
- Generalized division algorithm
- Radix representation and expansion of real numbers
- b-digital sequence
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Cite this paper
Hooshmand, M.H. (2013). b-Parts and finite b-representation of real numbers, Notes on Number Theory and Discrete Mathematics, 19(4), 4-15.