Simple Continued Fractions and Their Convergents

Bo Li; Yan Zhang; Artur Korniłowicz

Formalized Mathematics (2006)

  • Volume: 14, Issue: 3, page 71-78
  • ISSN: 1426-2630

Abstract

top
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.

How to cite

top

Bo Li, Yan Zhang, and Artur Korniłowicz. "Simple Continued Fractions and Their Convergents." Formalized Mathematics 14.3 (2006): 71-78. <http://eudml.org/doc/266747>.

@article{BoLi2006,
abstract = {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.},
author = {Bo Li, Yan Zhang, Artur Korniłowicz},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {71-78},
title = {Simple Continued Fractions and Their Convergents},
url = {http://eudml.org/doc/266747},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Bo Li
AU - Yan Zhang
AU - Artur Korniłowicz
TI - Simple Continued Fractions and Their Convergents
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 3
SP - 71
EP - 78
AB - 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.
LA - eng
UR - http://eudml.org/doc/266747
ER -

References

top
  1. [6] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  2. [7] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  3. [8] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990. 
  4. [9] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990. 
  5. [10] Jaroław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  6. [11] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. 
  7. [12] Robert M. Solovay. Fibonacci numbers. Formalized Mathematics, 10(2):81-83, 2002. 
  8. [13] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. 
  9. [14] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  10. [15] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. 
  11. [16] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990. 
  12. [17] Michal J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  13. [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  14. [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  15. [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  16. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  17. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  18. [3] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  19. [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  20. [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.