Commuting and Noncommuting Infinitesimals
暂无分享,去创建一个
[1] A. Connes. Noncommutative geometry and reality , 1995 .
[2] Mikhail G. Katz,et al. Zooming in on infinitesimal 1–.9.. in a post-triumvirate era , 2010, 1003.1501.
[3] Mikhail G. Katz,et al. A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography , 2011, 1104.0375.
[4] Margaret E. Baron,et al. The origins of the infinitesimal calculus , 1969 .
[5] Abraham Robinson,et al. On generalized limits and linear functionals. , 1964 .
[6] W. A. J. Luxemburg. What Is Nonstandard Analysis , 1973 .
[7] Eberhard Knobloch,et al. Leibniz's Rigorous Foundation Of Infinitesimal Geometry By Means Of Riemannian Sums , 2002, Synthese.
[8] Alexandre V. Borovik,et al. An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals , 2012, Notre Dame J. Formal Log..
[9] Lorenzo Magnani,et al. Mathematics through Diagrams: Microscopes in Non-Standard and Smooth Analysis , 2007, Model-Based Reasoning in Science, Technology, and Medicine.
[10] Herbert Meschkowski. Aus den Briefbüchern Georg Cantors , 1965 .
[11] Leif Arkeryd,et al. Intermolecular forces of infinite range and the Boltzmann equation , 1981 .
[12] K. D. Stroyan. Uniform Continuity and Rates of Growth of Meromorphic Functions1) , 1972 .
[13] E. Perkins. NONSTANDARD METHODS IN STOCHASTIC ANALYSIS AND MATHEMATICAL PHYSICS , 1988 .
[14] Mikhail G. Katz,et al. Ten Misconceptions from the History of Analysis and Their Debunking , 2012, 1202.4153.
[15] Mikhail G. Katz,et al. Meaning in Classical Mathematics: Is it at Odds with Intuitionism? , 2011, 1110.5456.
[16] M. Katz,et al. Two ways of obtaining infinitesimals by refining Cantor's completion of the reals , 2011, 1109.3553.
[17] David Sherry,et al. The wake of Berkeley's analyst: Rigor mathematicae? , 1987 .
[18] Hideyasu Yamashita,et al. Nonstandard Methods in Quantum Field Theory I: A Hyperfinite Formalism of Scalar Fields , 2002 .
[19] R. Ely. Nonstandard Student Conceptions About Infinitesimals , 2010 .
[20] D. Tall,et al. THE TENSION BETWEEN INTUITIVE INFINITESIMALS AND FORMAL MATHEMATICAL ANALYSIS , 2011, 1110.5747.
[21] Vladimir Kanovei,et al. Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics , 2012, 1211.0244.
[22] Jerzy Loś,et al. Quelques Remarques, Théorèmes Et Problèmes Sur Les Classes Définissables D'algèbres , 1955 .
[23] D. Laugwitz,et al. Eine Erweiterung der Infinitesimalrechnung , 1958 .
[24] Karin U. Katz,et al. When is .999... less than 1? , 2010, The Mathematics Enthusiast.
[25] Mikhail G. Katz,et al. Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond , 2012, 1205.0174.
[26] Edwin Hewitt,et al. Rings of real-valued continuous functions. I , 1948 .
[27] Alexandre Borovik,et al. Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus , 2011, 1108.2885.
[28] Philip Ehrlich,et al. The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes , 2006 .
[29] T. Skolem. Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen , 1934 .
[30] A. Cauchy. Cours d'analyse de l'École royale polytechnique , 1821 .
[31] H. Keisler. Elementary Calculus: An Infinitesimal Approach , 1976 .
[32] Lorenzo Magnani,et al. Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics , 2005 .
[33] S. Albeverio,et al. Singular Traces and Compact Operators , 1993, funct-an/9308001.
[34] M. Schützenberger,et al. Triangle of Thoughts , 2001 .
[35] Ekkehard Kopp,et al. On Cauchy's Notion of Infinitesimal , 1988, The British Journal for the Philosophy of Science.
[36] Numbers and models, standard and nonstandard , 2010 .
[37] A. Robinson. Non-standard analysis , 1966 .
[38] D. Tall. Looking at graphs through infinitesimal microscopes, windows and telescopes , 1980, The Mathematical Gazette.
[39] Edward Nelson. Internal set theory: A new approach to nonstandard analysis , 1977 .