Results 1 to 10 of about 146 (31)

Stevin numbers and reality [PDF]

, 2012
We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures.
A. H. Lightstone, A. L. Cauchy, A. Malet, A. Robinson, A. Tarski, A.-L. Cauchy, B. L. Waerden van der, C.S. Peirce, C.S. Peirce, D. Fearnley-Sander, D. H. Fowler, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sherry, D. Tall, D. Tall, E. Hewitt, G. Hellman, G. Lakoff, G. Schubring, H. Freudenthal, H. Sinaceur, J. Bair, J. Burgess, J. Dauben, J. Dauben, J. Havenel, J. L. Bell, K. Bråting, K. Katz, Karin Usadi Katz, L. Arkeryd, L. Arkeryd, L. Magnani, M. Moore, M. Moore, Mikhail G. Katz, N. Cutland, P. Ehrlich, P. Roquette, R. Dossena, R. Ely, R. Goldblatt, S. Gandz, Th. Skolem   +46 more
core   +1 more source

Consistency, non triviality and redundancy in mathematics [PDF]

, 2017
We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria, from the logic ...
Catsigeras, Eleonora
core   +3 more sources

Ten Misconceptions from the History of Analysis and Their Debunking [PDF]

, 2012
The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems.
A. Connes, A. Fraenkel, A. H. Lightstone, A. L. Cauchy, A. L. Cauchy, A. Malet, A. Robinson, A. Tarski, A. Weil, A. Weil, A.L. Cauchy, B. L. Waerden van der, B. Pourciau, B. Russell, C. Baltus, C. Boyer, D. E. Smith, D. Fearnley-Sander, D. H. Fowler, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sepkoski, D. Sherry, D. Sherry, D. Tall, D. Tall, David Sherry, E. Hewitt, E. Knobloch, E. Madison, E. Nelson, E.T. Bell, F. Faltin, F. W. Lawvere, G. Fisher, G. Leibniz, G. Schubring, H. Freudenthal, H. J. Keisler, H. J. M. Bos, H. Putnam, H. Rust, H. Sinaceur, Huygens, I. Grattan-Guinness, I. Kleiner, I. Lakatos, J. Crossley, J. Dauben, J. Grabiner, J. Gray, J. L. Bell, J. Lützen, J. Naets, K. Andersen, K. Bråting, K. Hrbacek, K. Hrbacek, K. Hrbáček, K. Katz, L. Arkeryd, L. Arkeryd, L. Magnani, M. Dehn, M. J. Barany, Mikhail G. Katz, N. Cutland, P. Ehrlich, P. Ehrlich, P. Giordano, P. Giordano, P. Mancosu, P. Mancosu, P. Roquette, P. Strømholm, Piotr Błaszczyk, R. Anderson, R. B. McClenon, R. Dedekind, R. Dedekind, R. Dossena, R. Ely, R. Lutz, S. Albeverio, S. H. Levy, S. Smale, T. Koetsier, T. Mormann, T. Tao, Th. Skolem, V. Benci, V. J. Katz, W. Felscher, W. Felscher   +95 more
core   +1 more source

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography [PDF]

, 2012
We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind ...
A. Alexander, A. H. Lightstone, A. Heyting, A. k. Weil, A. Robinson, A. Sfard, A.L. Cauchy, B.L. Waerden van der, Bruce Pourciau, Bruce Pourciau, C. Boyer, C. Jensen, D. Bridges, D. Fearnley-Sander, D. H. Fowler, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sepkoski, D. Sherry, D. Sherry, D. Tall, D. Tall, E. B. Davies, E. Bishop, E. Cousquer, E. Hewitt, E. Nelson, F. Richman, F. Smithies, G. Hellman, G. Hellman, G. Kreisel, G. M. Reyes, H. Billinge, H. Billinge, H. Breger, H. Freudenthal, H. Freudenthal, H. Meschkowski, H. Sinaceur, I. Barrow, J. Avigad, J. Bell, J. Burgess, J. Burgess, J. Burgess, J. Grabiner, J. Grabiner, J. Pierpont, J. Stillwell, K. Bråting, K. Katz, K. Rappaport, Karin Usadi Katz, L. A. Sad, L. Arkeryd, L. Arkeryd, L. Magnani, M. Dummett, M. Dummett, M. Mahoney, M. Moore, M. Moore, M. Muntersbjorn, Mikhail G. Katz, N. Cutland, P. Davis, P. Ehrlich, P. Giordano, P. Roquette, P.E.B. Jourdain, R. Dossena, R. Ely, R. Goldblatt, S. Gandz, S. Shapiro, S. Shapiro, S. Yablo, W. Ewald, W. Tait, W. Vincenti   +81 more
core   +1 more source

Leibniz's Laws of Continuity and Homogeneity

, 2012
We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target of numerous ...
Katz, Mikhail G., Sherry, David
core   +1 more source

General properties of Bayesian learning as statistical inference determined by conditional expectations [PDF]

, 2017
We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional ...
Gyenis, Zalán, Rédei, Miklós
core   +1 more source

Understanding and Calculating the Odds: Probability Theory Basics and Calculus Guide for Beginners, with Applications in Games of Chance and Everyday Life [PDF]

, 2006
This book presents not only the mathematical concept of probability, but also its philosophical aspects, the relativity of probability and its applications and even the psychology of probability.
Barboianu, Catalin
core  

A Cauchy-Dirac delta function

, 2012
The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal ...
A. Fraenkel, A. H. Lightstone, A. H. Lightstone, A.-L. Cauchy, A.-L. Cauchy, C. Boyer, C. S. Peirce, C. Schmieden, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sherry, David Tall, E. Hewitt, E. Nelson, G. Fisher, G. Fisher, G. Giorello, G. Takeuti, H. C. R. Méray, H. Keisler, H. Sinaceur, J. Dieudonné, J. Gray, J. Havenel, J. Lützen, K. Bråting, K. Katz, L. Arkeryd, L. Arkeryd, M. J. Barany, Mikhail G. Katz, N. Cutland, P. Dirac, P. Ehrlich, P. Giordano, P. Roquette, R. Ely, T. D. Todorov, Th. Skolem, Y. Péraire   +40 more
core   +1 more source

Karma Theory, Determinism, Fatalism and Freedom of Will [PDF]

, 2017
The so-called theory of karma is one of the distinguishing aspects of Hinduism and other non-Hindu south-Asian traditions. At the same time that the theory can be seen as closely connected with the freedom of will and action that we humans supposedly ...
Silvestre, Ricardo Sousa
core  

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

, 2012
Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory.
A. Fraenkel, A. H. Lightstone, A. L. Cauchy, A. Robinson, A. Robinson, A. Tarski, B. L. Waerden van der, B. Pourciau, B. Russell, C. Boyer, C. C. Gillispie, C. H. Edwards Jr, C. Schmieden, D. Fearnley-Sander, D. Fowler, D. Jesseph, D. Jesseph, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sherry, D. Sherry, D. Tall, D. Tall, D. Tall, David Sherry, E. Hewitt, E. Knobloch, E. Nelson, E. Strong, E. T. Bell, E. Zermelo, F. Cajori, F. W. Lawvere, G. Carchedi, G. Ferraro, G. Schubring, H. Freudenthal, H. Ishiguro, H. J. M. Bos, H. Kennedy, H. Rust, I. Grattan Guinness, I. Newton, J. Bair, J. Burgess, J. Earman, J. Grabiner, J. Gray, J. L. Bell, J. Wisdom, K. Andersen, K. Bråting, K. Katz, L. Arkeryd, L. Arkeryd, L. Jorgensen, L. Magnani, L. Narens, M. Horváth, M. Kline, Mikhail G. Katz, N. Bourbaki, N. Cutland, P. Ehrlich, P. Ehrlich, P. Mancosu, P. Mancosu, P. Roquette, R. Anderson, R. B. McClenon, R. Dossena, R. Ely, S. Albeverio, T. Rothman, T. Skolem, T. Tao   +76 more
core   +1 more source