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The b-parts of real numbers and the generalized division algorithm were considered and discussed in ⟦3⟧. Also some of their algebraic properties have been studied in ⟦4⟧. 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 paperAPA
Hooshmand, M.H. (2013). b-Parts and finite b-representation of real numbers, Notes on Number Theory and Discrete Mathematics, 19(4), 4-15.Chicago
Hooshmand, M.H. “b-Parts and Finite b-Representation of Real Numbers.” Notes on Number Theory and Discrete Mathematics 19, no. 4 (2013): 4-15.MLA
Hooshmand, M.H. “b-Parts and Finite b-Representation of Real Numbers.” Notes on Number Theory and Discrete Mathematics 19.4 (2013): 4-15. Print.