On the Representation of Natural Numbers in Positional Numeral Systems 1

Adam Naumowicz

Formalized Mathematics (2006)

  • Volume: 14, Issue: 4, page 221-223
  • ISSN: 1426-2630

Abstract

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In this paper we show that every natural number can be uniquely represented as a base-b numeral. The formalization is based on the proof presented in [11]. We also prove selected divisibility criteria in the base-10 numeral system.

How to cite

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Adam Naumowicz. " On the Representation of Natural Numbers in Positional Numeral Systems 1 ." Formalized Mathematics 14.4 (2006): 221-223. <http://eudml.org/doc/267383>.

@article{AdamNaumowicz2006,
abstract = {In this paper we show that every natural number can be uniquely represented as a base-b numeral. The formalization is based on the proof presented in [11]. We also prove selected divisibility criteria in the base-10 numeral system.},
author = {Adam Naumowicz},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {221-223},
title = { On the Representation of Natural Numbers in Positional Numeral Systems 1 },
url = {http://eudml.org/doc/267383},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Adam Naumowicz
TI - On the Representation of Natural Numbers in Positional Numeral Systems 1
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 4
SP - 221
EP - 223
AB - In this paper we show that every natural number can be uniquely represented as a base-b numeral. The formalization is based on the proof presented in [11]. We also prove selected divisibility criteria in the base-10 numeral system.
LA - eng
UR - http://eudml.org/doc/267383
ER -

References

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  11. [11] Wacław Sierpiński. Elementary Theory of Numbers. PWN, Warsaw, 1964. 
  12. [12] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. 
  13. [13] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. 
  14. [14] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  15. [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  16. [16] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001. 
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