[编辑] 参考文献
Alligood, Sauer, and Yorke(1996).“4.1 Cantor Sets”,Chaos: An introduction to dynamical systems.Springer.ISBN 0-387-94677-2.
Apostol, Tom M.(1974).Mathematical analysis,2e,Addison-Wesley.ISBN 0-201-00288-4.
Bartle, R.G. and D.R. Sherbert(1982).Introduction to real analysis.Wiley.ISBN 0-471-05944-7.
Beals, Richard(2004).Analysis.Cambridge UP.ISBN 0-521-60047-2.
Berlekamp, E.R.; J.H. Conway; and R.K. Guy(1982).Winning Ways for your Mathematical Plays.Academic Press.ISBN 0-12-091101-9.
Berz, Martin (1992). "Automatic differentiation as nonarchimedean analysis". Computer Arithmetic and Enclosure Methods: 439–450, Elsevier.
Bunch, Bryan H.(1982).Mathematical fallacies and paradoxes.Van Nostrand Reinhold.ISBN 0-442-24905-5.
Burrell, Brian(1998).Merriam-Webster's Guide to Everyday Math: A Home and Business Reference.Merriam-Webster.ISBN 0-87779-621-1.
Conway, John B.[1973](1978).Functions of one complex variable I,2e,Springer-Verlag.ISBN 0-387-90328-3.
Davies, Charles(1846).The University Arithmetic: Embracing the Science of Numbers, and Their Numerous Applications.A.S. Barnes.
DeSua, Frank C.(1970年1月). “A system isomorphic to the reals”(限制访问).The American Mathematical Monthly.67:900–903.
Dubinsky, Ed, Kirk Weller, Michael McDonald, and Anne Brown(2005年). “Some historical issues and paradoxes regarding the concept of infinity: an APOS analysis: part 2”.Educational Studies in Mathematics.60:253–266.DOI:10.1007/s10649-005-0473-0.
Edwards, Barbara and Michael Ward(2004年5月).“Surprises from mathematics education research: Student (mis)use of mathematical definitions”.The American Mathematical Monthly.111:411–425.
Enderton, Herbert B.(1977).Elements of set theory.Elsevier.ISBN 0-12-238440-7.
Euler, Leonhard[1770](1822).John Hewlett and Francis Horner, English translators. 编:Elements of Algebra,3rd English edition,Orme Longman.
Fjelstad, Paul(1995年1月). “The repeating integer paradox”(限制访问).The College Mathematics Journal.26:11–15.DOI:10.2307/2687285.
Gardiner, Anthony[1982](2003).Understanding Infinity: The Mathematics of Infinite Processes.Dover.ISBN 0-486-42538-X.
Gowers, Timothy(2002).Mathematics: A Very Short Introduction.Oxford UP.ISBN 0-19-285361-9.
Grattan-Guinness, Ivor(1970).The development of the foundations of mathematical analysis from Euler to Riemann.MIT Press.ISBN 0-262-07034-0.
Griffiths, H.B.,P.J. Hilton(1970).A Comprehensive Textbook of Classical Mathematics: A Contemporary Interpretation.London:Van Nostrand Reinhold.ISBN 0-442-02863-6. Template:LCC.
Kempner, A.J.(1970年1月). “Anormal Systems of Numeration”(限制访问).The American Mathematical Monthly.43:610–617.
Komornik, Vilmos; and Paola Loreti(1998年). “Unique Developments in Non-Integer Bases”(限制访问).The American Mathematical Monthly.105:636–639.
Leavitt, W.G.(1970年). “A Theorem on Repeating Decimals”(限制访问).The American Mathematical Monthly.74:669–673.
Leavitt, W.G.(1984年9月). “Repeating Decimals”(限制访问).The College Mathematics Journal.15:299–308.
Lewittes, Joseph(2006年).Midy's Theorem for Periodic Decimals.New York Number Theory Workshop on Combinatorial and Additive Number Theory.arXiv.
Lightstone, A.H.(1972年3月). “Infinitesimals”(限制访问).The American Mathematical Monthly.79:242–251.
Mankiewicz, Richard(2000).The story of mathematics.Cassell.ISBN 0-304-35473-2.
Maor, Eli(1987).To infinity and beyond: a cultural history of the infinite.Birkhäuser.ISBN 3-7643-3325-1.
Mazur, Joseph(2005).Euclid in the Rainforest: Discovering Universal Truths in Logic and Math.Pearson: Pi Press.ISBN 0-13-147994-6.
Munkres, James R.[1975](2000).Topology,2e,Prentice-Hall.ISBN 0-13-181629-2.
Pedrick, George(1994).A First Course in Analysis.Springer.ISBN 0-387-94108-8.
Petkovšek, Marko(1990年5月). “Ambiguous Numbers are Dense”(限制访问).American Mathematical Monthly.97:408–411.
Pinto, Márcia and David Tall (2001). "Following students' development in a traditional university analysis course". PME25: v4: 57–64.
Protter, M.H. and C.B. Morrey(1991).A first course in real analysis,2e,Springer.ISBN 0-387-97437-7.
Pugh, Charles Chapman(2001).Real mathematical analysis.Springer-Verlag.ISBN 0-387-95297-7.
Richman, Fred(1999年12月). “Is 0.999… = 1?”(限制访问).Mathematics Magazine.72(5):396–400.
Free HTML preprint: Richman, Fred(1999年6月8日).Is 0.999… = 1?.于2006年8月23日查阅.
Robinson, Abraham(1996).Non-standard analysis,Revised edition,Princeton University Press.ISBN 0-691-04490-2.
Rosenlicht, Maxwell(1985).Introduction to Analysis.Dover.ISBN 0-486-65038-3.
Rudin, Walter[1953](1976).Principles of mathematical analysis,3e,McGraw-Hill.ISBN 0-07-054235-X.
Shrader-Frechette, Maurice(1978年3月). “Complementary Rational Numbers”(限制访问).Mathematics Magazine.51:90–98.
Smith, Charles and Charles Harrington(1895).Arithmetic for Schools.Macmillan.
Sohrab, Houshang(2003).Basic Real Analysis.Birkhäuser.ISBN 0-8176-4211-0.
Stewart, Ian(1977).The Foundations of Mathematics.Oxford UP.ISBN 0-19-853165-6.
Stewart, James(1999).Calculus: Early transcendentals,4e,Brooks/Cole.ISBN 0-534-36298-2.
D.O. Tall and R.L.E. Schwarzenberger(1978年).“Conflicts in the Learning of Real Numbers and Limits”.Mathematics Teaching.82:44–49.
Tall, David(1976/7).“Conflicts and Catastrophes in the Learning of Mathematics”.Mathematical Education for Teaching.2:2–18.
Tall, David(2000年).“Cognitive Development In Advanced Mathematics Using Technology”.Mathematics Education Research Journal.12:210–230.
(德文)von Mangoldt, Dr. Hans(1911).“Reihenzahlen”,Einführung in die höhere Mathematik,1st ed.,Leipzig:Verlag von S. Hirzel.
Wallace, David Foster(2003).Everything and more: a compact history of infinity.Norton.ISBN 0-393-00338-8. |