biblografy for rational numbers
Answers
Answer: [A’C] Norbert A’Campo, A natural construction for the real numbers.
arXiv:math.GN/0301015.
[Apo67] Tom M. Apostol, Calculus. Vol. I: One-Variable Calculus, with an Introduction to
Linear Algebra, 2nd ed., Blaisdell, Waltham, MA, 1967.
[AH01] Jorg Arndt and Christoph Haenel, ¨ Pi—Unleashed, 2nd ed., Springer-Verlag, Berlin,
2001. Translated from the 1998 German original by Catriona Lischka and David
Lischka.
[Art64] Emil Artin, The Gamma Function, Translated by Michael Butler. Athena Series:
Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1964.
[Bar69] Margaret E. Baron, The Origins of the Infinitesimal Calculus, Pergamon Press,
Oxford, 1969.
[Bar96] Robert G. Bartle, Return to the Riemann integral, Amer. Math. Monthly 103 (1996),
no. 8, 625–632.
[Bea97] Alan F. Beardon, Limits: A New Approach to Real Analysis, Springer-Verlag, New
York, 1997.
[BBB04] Lennart Berggren, Jonathan Borwein, and Peter Borwein, Pi: A Source Book, 3rd
ed., Springer-Verlag, New York, 2004.
[BML] Garrett Birkhoff and Saunders Mac Lane, A Survey of Modern Algebra, 3rd ed.,
Macmillan, New York.
[Blo00] Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics,
Birkhauser, Boston, 2000. ¨
[Blo10] , Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd
ed., Springer-Verlag, New York, 2010.
[Bol78] Vladimir G. Boltianski˘ı, Hilbert’s Third Problem, V. H. Winston & Sons, Washington, DC, 1978. Translated from the Russian by Richard A. Silverman; With a
foreword by Albert B. J. Novikoff; Scripta Series in Mathematics.
[BD09] William Boyce and Richard DiPrima, Elementary Differential Equations and
Boundary Value Problems, 9th ed., John Wiley & Sons, New York, 2009.
Step-by-step explanation: PLEASE MAKE ME THE BRAINLEIST
Answer:
A one-to-one correspondence between positive binary numbers and positive rational numbers is defined and studied. Efficient algorithms to compute the rational number for a given binary ordinal number and to compute the binary ordinal number for a given rational number are presented and analyzed. This one-to-one correspondence and the related algorithms provide a link between the well-known problem of counting rational numbers and a key topic in computer science: binary numbers. The binary ordinal number of a rational and that of its reciprocal are shown to be related in a simple manner.