# On the Representation of Natural Numbers in Positional Numeral Systems 1

Formalized Mathematics (2006)

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

## Access Full Article

top## Abstract

top## How to cite

topAdam 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

top- [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [4] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
- [5] Rafał Kwiatek. Factorial and Newton coeffcients. Formalized Mathematics, 1(5):887-890, 1990.
- [6] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.
- [7] Karol Pak. Stirling numbers of the second kind. Formalized Mathematics, 13(2):337-345, 2005.
- [8] Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125-130, 1991.
- [9] Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
- [10] Konrad Raczkowski and Andrzej Nędzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991.
- [11] Wacław Sierpiński. Elementary Theory of Numbers. PWN, Warsaw, 1964.
- [12] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
- [13] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
- [14] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [16] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
- [17] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.