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Relevant bibliographies by topics / Mathematics / Infinity

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Academic literature on the topic 'Mathematics / Infinity'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 January 2023

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Journal articles on the topic "Mathematics / Infinity"

1

Love, William P. "Infinity: The Twilight Zone of Mathematics." Mathematics Teacher 82, no. 4 (1989): 284–92. http://dx.doi.org/10.5951/mt.82.4.0284.

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The concept of infinity has fascinated the human race for thousands of years. Who among us has never been awed by the mysterious and often paradoxical nature of the infinite? The ancient Greeks were fascinated by infinity, and they struggled with its nature. They left for us many unanswered questions including Zeno's famous paradoxes. The concept of infinity is with us today, and many ideas in modern mathematics are dependent on the infinitely large or the infinitely small. But most people's ideas about infinity are very vague and unclear, existing in that fuzzy realm of the twilight zone

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Burgin, Mark. "Introduction to Hyperspaces." International Journal of Pure Mathematics 7 (February 8, 2021): 36–42. http://dx.doi.org/10.46300/91019.2020.7.5.

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The development of mathematics brought mathematicians to infinite structures. This process started with transcendent real numbers and infinite sequences going through infinite series to transfinite numbers to nonstandard numbers to hypernumbers. From mathematics, infinity came to physics where physicists have been trying to get rid of infinity inventing a variety of techniques for doing this. In contrast to this, mathematicians as well as some physicists suggested ways to work with infinity introducing new mathematical structures such distributions and extrafunctions. The goal of this paper is

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Salanskis, Jean-Michel. "Ways of Infinity." Studies in Logic, Grammar and Rhetoric 44, no. 1 (2016): 169–80. http://dx.doi.org/10.1515/slgr-2016-0010.

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Abstract The paper discusses analogies between the way in which infinity is understood and dealt with in mathematics and in Jewish tradition. It begins with recalling the classical debate about infinity in the field of the foundations of mathematics. Reading an important paper by A. Robinson, we come to the conclusion that mathematicians work “as if” infinite totalities existed. They do so by following the rules of their formalized discourse which, at least if it refers to anything at all, also refers to such totalities. The paper describes how, according to Jewish tradition, infinity is also

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Hong, Zhang. "Dialectical Infinity and the Third Mathematical Crisis —On the Fundamental Error of Actual Infinity." Journal of Research in Philosophy and History 3, no. 2 (2020): p73. http://dx.doi.org/10.22158/jrph.v3n2p73.

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This paper discusses the problem of finity and infinity based on the philosophical perspectives of opposing idealism and receiving dialectical materialism. Based on Hegel’s dialectical infinity view, this paper makes a comprehensive criticism of the thought of actual infinity. After Hegel’s dialectical infinite thought scientifically explained the limit concept in calculus, the Second Mathematical Crisis caused by the contradiction of infinitesimal quantity was solved thoroughly. However, the mathematics world has not learned the experience and lessons in history, has always adhered to the ide

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Blanc, Jill Le. "Infinity in Theology and Mathematics." Religious Studies 29, no. 1 (1993): 51–62. http://dx.doi.org/10.1017/s0034412500022046.

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Can we apply the same concepts to both the finite and the infinite? Is there something distinctive about the infinite that prevents attribution to it of concepts that we can attribute to the finite? If so, then this could be a reason for our difficulties in talking about God – God is infinite, and our concepts, applying, as they do, to the finite objects of our experience, cannot be ‘extended’ to the infinite. God's infinity is sometimes used as an explanation of theological difficulties like the problem of evil or the paradoxes of omnipotence: we do not really know what we mean when we attrib

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Scott, David D. "The boundless riches of God." Theology in Scotland 27, no. 2 (2020): 25–41. http://dx.doi.org/10.15664/tis.v27i2.2138.

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This paper explores the concept of infinity in mathematics and its relation to theological considerations. It begins by seeking to answer the question of whether mathematical enquiry into the character of infinity may cast some light on the infinite character of God. Drawing on the work of Euclid, Cantor, and Gödel in particular, it considers concepts of potential and actual infinity and how mathematical discoveries have implications for (i) the relation of the finite and infinite (which has theological implications for the incarnation); (ii) the relation of theory and reality; (iii) the futur

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Zarepour, Mohammad Saleh. "Avicenna on Mathematical Infinity." Archiv für Geschichte der Philosophie 102, no. 3 (2020): 379–425. http://dx.doi.org/10.1515/agph-2017-0032.

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AbstractAvicenna believed in mathematical finitism. He argued that magnitudes and sets of ordered numbers and numbered things cannot be actually infinite. In this paper, I discuss his arguments against the actuality of mathematical infinity. A careful analysis of the subtleties of his main argument, i. e., The Mapping Argument, shows that, by employing the notion of correspondence as a tool for comparing the sizes of mathematical infinities, he arrived at a very deep and insightful understanding of the notion of mathematical infinity, one that is much more modern than we might expect. I argue,

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Feferman, Solomon. "Infinity in Mathematics." Philosophical Topics 17, no. 2 (1989): 23–45. http://dx.doi.org/10.5840/philtopics19891722.

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Murawski, Roman. "Mathematics and Theology in the Thought of Nicholas of Cusa." Logica Universalis 13, no. 4 (2019): 477–85. http://dx.doi.org/10.1007/s11787-019-00232-2.

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Abstract Nicholas of Cusa was first of all a theologian but he was interested also in mathematic and natural sciences. In fact philosophico-theological and mathematical ideas were intertwined by him, theological and philosophical ideas influenced his mathematical considerations, in particular when he considered philosophical problems connected with mathematics and vice versa, mathematical ideas and examples were used by him to explain some ideas from theology. In this paper we attempt to indicate this mutual influence. We shall concentrate on the following problems: (1) the role and place of m

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Kolman, Vojtěch. "Hegel’s ‘Bad Infinity’ as a Logical Problem." Hegel Bulletin 37, no. 2 (2016): 258–80. http://dx.doi.org/10.1017/hgl.2016.18.

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AbstractThe paper analyses the concept of ‘bad infinity’ in connection with Hegel’s critique of infinitesimal calculus and with the belittling of Hegel’s mathematical notions by the representatives of modern logic and the foundations of mathematics. The main line of argument draws on the observation that Hegel’s difference is only derivatively a mathematical one and is primarily of a broadly logico-epistemological nature. Because of this, the concept of bad infinity can be fruitfully utilized, by way of inversion, in an analysis of the conceptual shortcomings of the most prominent foundational

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Dissertations / Theses on the topic "Mathematics / Infinity"

1

Ackerman, Nathaniel Leedom. "Quantifier rank spectrum of L-infinity-omega." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34269.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Includes bibliographical references (p. 321) and index.<br>In Part A we will study the quantifier rank spectrum of sentences of L!1,!. We will show that there are scattered sentences with models of arbitrarily high but bounded quantifier rank. We will also consider the case of weakly scattered and almost scattered sentences, and we will make some conjectures. I

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Nardin, Denis Ph D. Massachusetts Institute of Technology. "Stability and distributivity over orbital [infinity]-categories/." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112895.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.<br>In title on title-page, "[infinity]" appears as the symbol. Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 64-66).<br>Let G be a finite group. The homotopy theory of topological spaces with an action of G has provided important applications in many parts of homotopy theory and geometry. An especially important role has been played by the so-called "norm maps". In this thesis we develop a characterization of the [infinity]-category of G-spectra and of its multiplicativ

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Daily, Marilyn Elizabeth. "L(Infinity) Structures on Spaces of Low Dimension." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-04132004-155423/.

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L(Infinity) structures are natural generalizations of Lie algebras, which need satisfy the standard graded Jacobi identity only up to homotopy. They have also been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This dissertation classifies all possible L(Infinity) structures which can be constructed on a Z-graded (characteristic 0) vector space of dimension three or less. It also includes necessary and sufficient conditions under which a space with an L(3) structure is a differential graded Lie algebra. Additionally, it is shown that some

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Monaghan, J. "Adolescents' understanding of limits and infinity." Thesis, University of Warwick, 1986. http://wrap.warwick.ac.uk/34626/.

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AIM To investigate mathematically able adolescents' conceptions of the basic notions behind the Calculus: infinity (including the infinitely large, the infinitely small and infinite aggregates); limits (of sequences, series and functions); and real numbers. To observe the effect, if any, on these conceptions, of a one year calculus course. EXPERIMENTS Pilot interviews and questionnaires helped identify areas on which to focus the study. A questionnaire was administered to Lower Sixth Form students with 0-level mathematics passes. The questionnaire was administered twice, once in September and

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Lorent, Andrew. "Rectifiability results for some measures in #iota#'3#infinity#." Thesis, University College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368158.

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Peery, Thaddeus Eldon. "H(Infinity) optimal repetitive control : continuous-time and sampled-data formulations /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487864485231418.

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韓祖淵 and Cho-yuen Han. "A unified game theory approach to H-infinity control and filtering." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235815.

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Han, Cho-yuen. "A unified game theory approach to H-infinity control and filtering /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18635520.

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Hohberger, Horst. "Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity." Phd thesis, Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2007/1157/.

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Li, Jiayong Ph D. Massachusetts Institute of Technology. "A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101822.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 253-254).<br>For a Lagrangian submanifold, we define a moduli space of trees of holomorphic disk maps with Morse flow lines as edges, and construct an ambient space around it which we call the quotient space of disk trees. We show that this ambient space is an M-polyfold with boundary and corners by combining the infinite dimensional analysis in sc-Banach space with the finite dimensional analysis in Deligne-Mumford space

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Books on the topic "Mathematics / Infinity"

1

Wallace, David Foster. Everything and more: A compact history of infinity. Atlas Book, 2010.

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2

Infinity explained. Rosen Publishing, 2015.

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Faticoni, Theodore G. The Mathematics of Infinity. John Wiley & Sons, Ltd., 2006.

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Faticoni, Theodore G. The Mathematics of Infinity. John Wiley & Sons, Inc., 2006. http://dx.doi.org/10.1002/0470049146.

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Faticoni, Theodore G. The Mathematics of Infinity. John Wiley & Sons, Inc., 2012. http://dx.doi.org/10.1002/9781118243879.

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The mathematics of infinity: A guide to great ideas. 2nd ed. John Wiley & Sons, 2012.

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Infinity: New research frontiers. Cambridge University Press, 2011.

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Aristotle, ed. Aristotle on mathematical infinity. F. Steiner, 1995.

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9

Rucker, Rudy v. B. Infinity and the mind: The science and philosophy of the infinite. Princeton University Press, 2005.

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10

Whitaker's almanack little book of infinity. A. & C. Black, 2006.

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Book chapters on the topic "Mathematics / Infinity"

1

Çevik, Ahmet. "Infinity." In Philosophy of Mathematics. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003223191-9.

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Mortensen, Chris. "Modulo Infinity." In Inconsistent Mathematics. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8453-1_3.

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Gray, Jeremy. "Mathematics at infinity." In Mathematics, Substance and Surmise. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21473-3_11.

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Martin-Löf, Per. "Mathematics of infinity." In COLOG-88. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/3-540-52335-9_54.

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Franklin, James. "Infinity." In An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan UK, 2014. http://dx.doi.org/10.1057/9781137400734_9.

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Lindqvist, Peter. "The Infinity Laplacian." In SpringerBriefs in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14501-9_8.

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Stillwell, John. "Infinity in Greek Mathematics." In Undergraduate Texts in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55193-3_4.

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Stillwell, John. "Infinity in Greek Mathematics." In Undergraduate Texts in Mathematics. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4684-9281-1_4.

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Stillwell, John. "Infinity in Greek Mathematics." In Undergraduate Texts in Mathematics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6053-5_4.

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Stillwell, John. "Infinity in Greek Mathematics." In Undergraduate Texts in Mathematics. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4899-0007-4_4.

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Conference papers on the topic "Mathematics / Infinity"

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Sergeyev, Yaroslav D., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Infinity Computer and Calculus." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790118.

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PARKER, MATTHEW. "PHILOSOPHICAL METHOD AND GALILEO'S PARADOX OF INFINITY." In Essays in Philosophy and History of Mathematics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812812230_0004.

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Georgiev, Georgi Hristov, and Vencislav Dakov Radulov. "Epipolar geometry with one epipole at infinity." In 39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS AMEE13. AIP, 2013. http://dx.doi.org/10.1063/1.4854779.

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Herlambang, Teguh, Abdul Muhith, Irhamah, Mohamad Yusak Anshori, Dinita Rahmalia, and Denis Fidita Karya. "Implementation of H-infinity and ensemble Kalman filter for whole blood (WB) estimation in PMI Bojonegoro." In PROCEEDINGS OF THE 6TH NATIONAL CONFERENCE ON MATHEMATICS AND MATHEMATICS EDUCATION. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0096121.

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Mukhametzhanov, Marat S., and Yaroslav D. Sergeyev. "The infinity computer vs. symbolic computations: First steps in comparison." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026820.

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Kalogiratou, Z., Th Monovasilis, T. E. Simos, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Symplectic Runge-Kutta-Nyström Methods with Phase-Lag Order Six and Infinity." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498573.

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Papadopoulos, D. F., T. E. Simos, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "A Modified RKN with Infinity Order of Phase-lag Derivative for the Numerical Integration of ODEs with Oscillating Solutions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637015.

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Tarulli, Mirko. "On the well-posedness of perturbed wave equation with nonlinearity vanishing at infinity: Linear theory." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902481.

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Georgiev, Georgi Hristov, and Vencislav Dakov Radulov. "On the epipolar geometry with two coincident projection planes and two coincident epipoles at infinity." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902502.

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Djondjorov, P. A., D. M. Dantchev, and V. M. Vassilev. "Exact results for the Casimir force in a model with Neumann-infinity boundary conditions." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’17. Author(s), 2017. http://dx.doi.org/10.1063/1.5007401.

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Reports on the topic "Mathematics / Infinity"

1

Schmid, Rudolf. Infinite Dimentional Lie Groups With Applications to Mathematical Physics. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-1-2004-54-120.

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