Results 21 to 30 of about 1,578 (68)

Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow [PDF]

, 2014
Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer.
David Sherry, Emanuele Bottazzi, Emanuele Bottazzi, Frederik Herzberg, Karin U. Katz, Mikhail G. Katz, Ph. D. Università, Steven Shnider, Tahl Nowik, Tiziana Bascelli, Vladimir Kanovei   +10 more
core   +3 more sources

Changing a semantics: opportunism or courage?

, 2014
The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic.
A. Chagrov, A. Gil-Luezas, A. Mann, A. Mostowski, A. Pasztor, B. Davey, B. Ganter, B. Jónsson, B. ten Cate, D. Cantone, D. Gallin, D. Harel, D. Hilbert, D. Kozen, E. Bishop, E. Lopez-Escobar, G. Bezhanishvili, G. Sambin, H. Andréka, H. Andréka, H. Andréka, H. Andréka, H. Enderton, H.-D. Ebbinghaus, H.A. Priestley, H.A. Priestley, I. Walukiewicz, J. Akkanen, J. Barwise, J. Barwise, J. Barwise, J. Benthem van, J. Benthem van, J. Benthem van, J. Benthem van, J. Benthem van, J. Benthem van, J. Benthem van, J. Hintikka, J. Madarász, J. Väänänen, J. Väänänen, J. Väänänen, K. Kunen, L. Csirmaz, L. Esakia, L. Henkin, L. Henkin, L. Henkin, L. Henkin, L. Henkin, L. Henkin, L. Henkin, L. Henkin, L. Humberstone, L. Santocanale, L. Santocanale, M. Dunn, M. Dunn, M. Gehrke, M. Kracht, M. Manzano, M. Manzano, M.O. Rabin, N. Bezhanishvili, N. Bezhanishvili, N. Galatos, P. Blackburn, P. Hájek, R. Kaye, R. Montague, R.L. Vaught, S. Ambler, S. Feferman, S. Simpson, S.K. Thomason, T. Gergely, T. Hyttinen, V. Marra, V. Stebletsova, W. Blok, W. Holliday, W. Walkoe, Y. Venema, Y. Venema   +84 more
core   +1 more source

Axiomatics for the external numbers of nonstandard analysis [PDF]

, 2017
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix.
Berg, Imme van den, Dinis, Bruno
core   +2 more sources

Structure and Computation

Noûs, EarlyView.
ABSTRACT It is a truism of mathematics that differences between isomorphic number systems are irrelevant to arithmetic. This truism is deeply rooted in the modern axiomatic method and underlies most strands of arithmetical structuralism, the view that arithmetic is about some abstract number structure.
Balthasar Grabmayr
wiley   +1 more source

Arithmetic, Set Theory, Reduction and Explanation [PDF]

, 2018
Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress.
D’Alessandro, William
core  

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

, 2017
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing ...
A Alexander, A Borovik, A Kock, A Robinson, A Tarski, AL Cauchy, AL Cauchy, AL Cauchy, Alexandre Borovik, C Boyer, C Fraser, C Fraser, C Schmieden, D Laugwitz, D Laugwitz, D Spalt, David M. Schaps, David Sherry, E Giusti, E Hewitt, E Nelson, G Arsac, G Ferraro, G Fisher, H Bos, H Bosmans, H Edwards, H Ishiguro, H Sørensen, I Grattan-Guinness, J Bell, J Cleave, J Earman, J Grabiner, J Grabiner, J Grabiner, J Gray, J-P Ramis, K Easwaran, K Katz, K Katz, K Viertel, Karin U. Katz, M Hellyer, M Katz, M Katz, M Katz, M Katz, M McKinzie, M McKinzie, M Nakane, M Wartofsky, Mikhail G. Katz, N Cutland, P Benacerraf, P Błaszczyk, P Halmos, P Mancosu, Piotr Błaszczyk, R Bradley, S Unguru, Semen S. Kutateladze, T Bascelli, T Kuhn, T Tao, Thomas McGaffey, Tiziana Bascelli, V Kanovei, V Kanovei, Vladimir Kanovei, W Quine, Y Sergeyev   +71 more
core   +1 more source

Hypernatural Numbers as Ultrafilters [PDF]

, 2015
In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of ...
A Blass, C Puritz, C Puritz, CC Chang, D Ballard, G Cherlin, G Choquet, H Cartan, HJ Keisler, J Hirshfeld, J van Mill, K Hrbác̆ek, K Kunen, L Haddad, L Luperi Baglini, M Beiglböck, M Nasso Di, M Nasso Di, N Hindman, N Hindman, N Hindman, N Hindman, P Komjáth, R Ellis, R Graham, V Kanovei, WAJ Luxemburg, WW Comfort   +27 more
core   +2 more sources

Exploring 2D Geometric Shape Classification Using AI‐Driven Feature Tables in Mathematics

School Science and Mathematics, EarlyView.
ABSTRACT This study explored the effectiveness of an AI‐integrated instructional task designed to enhance preservice teachers' understanding of the features and hierarchical relationships of 2D geometric shapes. Originally developed and tested in online K‐12 professional development settings, this intervention was adapted for in‐person preservice ...
Yasemin Gunpinar, Woonhee Sung
wiley   +1 more source

Ultrafast Adhesion/Friction Bidirectionally Switchable Control by Vibration

Advanced Functional Materials, Volume 36, Issue 8, 26 January 2026.
Bioinspired gradient smooth architectures enable vibration‐switchable adhesion/friction with 62.02 kPa adhesion strength, 131.57 kPa shear strength, tilt angles ≥ 3°, roughness ≥ Ra 0.8 µm, 400 Hz antivibration robustness, and dual‐mode control. The synergy of geometry optimization and vibration modulation tuning bridges multidomain adaptability and ...
Jian Chen, Wenjie Chen, Mengmeng Zhao, Xingyu Jiang, Xiaolei Zhu, Xinran Xu, Jiahui Zhao, Yezhong Tang, Stanislav N Gorb, Keju Ji, Zhendong Dai   +10 more
wiley   +1 more source

Grilliot's trick in Nonstandard Analysis

, 2017
The technique known as Grilliot's trick constitutes a template for explicitly defining the Turing jump functional $(\exists^2)$ in terms of a given effectively discontinuous type two functional. In this paper, we discuss the standard extensionality trick:
Sanders, Sam
core   +1 more source