On the Representation of Natural Numbers in Positional Numeral Systems¹

• Autorzy: Adam Naumowicz
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2006
• Tom: 14
• Numer: 4
• Strony: 221-223

Daty

wydano

2006-01-01

online

2008-06-13

Twórcy

autor

Adam Naumowicz

• Institute of Computer Science, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

Bibliografia

• [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.

Identyfikatory

DOI

10.2478/v10037-006-0025-9