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• # Artykuł - szczegóły

## Formalized Mathematics

2006 | 14 | 3 | 71-78

## Simple Continued Fractions and Their Convergents

EN

### Abstrakty

EN
The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.

71-78

wydano
2006-01-01
online
2008-06-09

### Twórcy

autor
• Qingdao University of Science and Technology, China
autor
• Qingdao University of Science and Technology, China
autor
• Institute of Computer Science, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland

### Bibliografia

• [6] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [7] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
• [8] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.
• [9] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.
• [10] Jaroław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
• [11] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
• [12] Robert M. Solovay. Fibonacci numbers. Formalized Mathematics, 10(2):81-83, 2002.
• [13] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
• [14] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
• [15] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
• [16] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
• [17] Michal J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
• [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
• [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
• [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
• [3] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
• [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.