Title variants
Languages of publication
Abstracts
An unrestricted division by zero implemented as an algebraic multiplication by infinity is feasible within a multispatial hyperspace comprising several quasigeometric spaces.
Discipline
Publisher
Journal
Year
Volume
Issue
Pages
171-197
Physical description
Contributors
author
- Science/Mathematics Education Department, Southern University and A&M College, Baton Rouge, LA 70813, USA
References
- [1] Chevalley C. The algebraic theory of spinors and Clifford algebras. Berlin: Springer, 1997, p. 86f.
- [2] Jacobson N. Lectures in abstract algebra II: Linear algebra, Princeton, NJ: Nostrand, 1953, p. 54.
- [3] Lomov S.A. Introduction to the general theory of singular perturbations. Providence, RI: AMS, 1992, p. 296.
- [4] Ramis J.-P. & Ruget G. Complexe dualisant et théorèmes de dualité en géométrie analytique complexe. IHES Publ. Math. 38 (1970) 77-91
- [5] Cartan E. Le principe de dualité et certaines intégrales multiples de l’espace tangentiel et de l’espace réglé. [pp. 265-302 in : Cartan E. : Oeuvres complètes. T.1 pt.2. Paris : Gauthier-Villars, 1953].
- [6] Gruenberg K.W. & Weir A.J. Linear geometry. New York: Springer, 1977, p. 86.
- [7] Lautman A. Symétrie at dissymétrie en mathématiques et la physique. [pp. 54-65 in: Le Lionnais F. Les grands courants de la pensée mathématique. Paris : Editions des «Cahiers du Sud», 1948].
- [8] Simon M. Nichteuklidische Geometrie in elementarer Behandlung. Leipzig: Teubner, 1925, p. 32.
- [9] Eves H. An introduction to the history of mathematics. New York: Holt, Rinehart and Winston, 1976, p. 306.
- [10] Euler L. Elements of algebra. New York: Springer, 1984, p. 22f.
- [11] Czajko J. On Cantorian Spacetime over Number Systems with Division by Zero. Chaos Solit. Fract. 21 (2004) 261-271 https://www.plover.com/misc/CSF/sdarticle(2).pdf
- [12] Couturat L. De L’infini mathématique. New York: Burt Franklin, 1969, pp. 99, 254, 278, 435.
- [13] Rotman B. Signifying nothing. The semiotics of zero. Stanford, CA: Stanford Univ. Press, 1993, p. 73.
- [14] Mathews J.H. & Howell R.W. Complex analysis for mathematics and engineering. New Delhi: Jones and Bartlett, 2011, p. 273ff.
- [15] Knopp K. Elements of the theory of functions. Part 2: Applications and continuation of the general theory. New York: Dover, 1947, pp. IX, 35.
- [16] Curtiss D.R. Analytic functions of a complex variable. La Salle, IL: Open Court Publishing, 1948, p. 91.
- [17] Birkhoff G.D. The foundations of quantum mechanics. [pp. 857-875 in: Birkhoff G.D. (Ed.) Collected mathematical papers II. New York: Dover, 1968, see p. 865].
- [18] Birkhoff G.D. & Kellogg O.D. Invariant points in function space. [pp. 255-274 in: Birkhoff G.D. (Ed.) Collected mathematical papers III. New York: Dover, 1968, see p. 255].
- [19] Lesh R. et al. Model development sequences. [pp. 35-58 in: Lesh R. & Doerr H.M. Beyond constructivism. Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates, Publishers, 2003, see p. 36].
- [20] Dieudonné J. Treatise on analysis II. New York: Academic Press, 1970, p. 151ff.
- [21] Šurygin, V.A. Constructive sets with equality and their mappings. [in: Orevkov V.P. & Šanin N.A. (Eds.) Problems in the constructive mathematics: V. Proc. Steklov Inst. Math. 113 (1970) p. 195].
- [22] Kyrala A. Applied functions of a complex variable. New York: Wiley-Interscience, 1972, p. 5f.
- [23] Šanin N.A. Constructive real numbers and constructive function spaces. Providence, RI: AMS, 1968, pp. 305f, 307.
- [24] Michiwaki H., Saitoh S. & Yamada M. Reality of the division by zero z/0=0. Int. J. Appl. Phys. Math. 6(1) (2016) 1-8 http://www.ijapm.org/show-63-504-1.html
- [25] Michiwaki H, Okumura H. & Saitoh S. Division by Zero z=0 = 0 in Euclidean Spaces. Int. J. Math. Computation, 28(1) (2017) 1-16 http://www.ceser.in/ceserp/index.php/ijmc/article/view/4663
- [26] Gelbaum B.R. & Olmsted J.M.H. Counterexamples in analysis. Mineola, NY: Dover, 2003, pp. 4, 7.
- [27] Flanders H. Calculus. New York: W.H. Freeman & Co., 1985, p. 134ff.
- [28] Ribenboim P. Functions, limits and continuity. New York: Wiley, 1964, p. 69.
- [29] Osserman R. Two-dimensional calculus. Huntington, NY: Robert E. Krieger Publishing, 1977, p. 253.
- [30] Alt H.W. Lineare Funktionalanalysis. Berlin: Springer, 1985, p. 87.
- [31] Ben-Israel A. & Greville T.N.E. Generalized inverses. Theory and applications. New York: Springer, 2003, p. 356ff.
- [32] Köthe G. Topological vector spaces II. New York: Springer, 1979, p. 114f.
- [33] Volterra V. Leçons sur les fonctions des lignes. Paris : Gauthier-Villars, 1913, p. 38.
- [34] Morley F. & Morley F.V. Inversive geometry. New York: Chelsea Publishing, 954, pp. 44, 39.
- [35] Bakel’man I.Ya. Inversions. Chicago: The Univ. of Chicago Press, 1974, 8f.
- [36] Saks S. & Zygmund A. Analytic functions. Warsaw: PWN, 1971, p.14ff, p. 254.
- [37] Hille E. Analytic Function Theory I. New York: Chelsea Publishing, 1973, p. 47.
- [38] Dieudonné J. Treatise on analysis III. New York: Academic Press, 1972, p. 132ff.
- [39] Richardson L.F. Measure and integration. A concise introduction to real analysis. Hoboken, NJ: Wiley, 2009, p. 174ff.
- [40] Abian A. The theory of sets and transfinite arithmetic. Philadelphia, PA: Saunders, 1965, p. 126.
- [41] Eilenberg S. & MacLane S. General theory of natural equivalences. [pp. 273-336 in: Kaplansky I. (Ed.) Saunders MacLane selected papers. New York: Springer, 1979, see p. 274f].
- [42] Salas S.L. & Hille E. Calculus. One and several variables. New York: Wiley, 1990, pp. 591, 597.
- [43] Weyl H. Die heutige Erkenntnislage in der Mathematik. Erlangen, 1926, p. 1.
- [44] Weyl H. Stufen des Unendlichen. Jena, 1931, p. 1.
- [45] Delachet A. Contemporary geometry. New York: Dover, 1962, p. 37.
- [46] Coxeter H.S.M. Projective geometry. New York: Blaisdell Publishing, 1964, pp. 25ff.
- [47] Coxeter H.S.M. The real projective plane. New York: McGraw-Hill, 1949, p. 4f.
- [48] Cartan E. Géométrie projective et géométrie riemannienne. [pp. 1155-1166 in: E. Cartan Oeuvres complètes. T.2 Pt.3. Paris : Gauthier-Villars, 1955].
- [49] Klein F. On the so-called noneuclidean geometry. [pp. 69-111 in: Stillwell J. (Ed.) Sources of hyperbolic geometry. Providence, RI: AMS, 1996, see p. 109f].
- [50] Dodge C.W. Euclidean geometry and transformations. Reading, MA: Addison-Wesley, 1972, p. 9.
- [51] Von Neumann J. Continuous geometry. Princeton, NJ: Princeton Univ. Press, 1960, pp. 16, 40.
- [52] Lie M.S. On a class of geometric transformations. [in: Smith D.E. A source book in mathematics 2. New York: Dover, 1959, p. 487].
- [53] Cartan H. Théorie élémentaire des fonctions analytiques d’une ou plusieurs variables complexes. Paris : Hermann, 1961, p. 90ff.
- [54] Cantor G. Georg Cantor gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Hildesheim, 1966, p. 165ff.
- [55] Klein F. Elementary mathematics from an advanced standpoint. New York, 1939, p.54ff.
- [56] Holder O. Die mathematische Methode. Berlin, 1924, p. 556.
- [57] Sinnige T.G. Matter and infinity in the presocratic schools and Plato. Assen, 1971, p. 151.
- [58] Thom R. Quid des stratifications canoniques. [p. 375-381 in: Brasselet J.-P. (Ed.) Singularities. Lille 1991. Cambridge: Cambridge Univ. Press, 1994, see p. 376].
- [59] Visnievsky D. A unified approach to external and internal symmetries. Int. J. Mod. Phys. A 15 (2000) 3733-3738
- [60] Boyer C.B. The history of the calculus and its conceptual development. New York: Dover, 1959, p. 249.
- [61] Tartar L. From hyperbolic systems to kinetic theory. A personalized quest. Berlin: Springer, 2008, p. 4.
- [62] Thom R. Modelès mathématiques de la morphogenèse. Paris : Christian Burgeois Éditeur, 1980, p. 292.
- [63] Le Lionnais F. Les grands courants de la pensée mathématique. Cahiers du Sud 48, p. 188.
- [64] Poole E.G.C. Introduction to the theory of linear differential equations. Oxford: At The Univ. Press, 1936, p. 74.
- [65] Cranga R. Postulat D’Euclide = d/0. Paris : Verites Nouvelles, 1969, pp. 7, 18.
- [66] Vullemin J. La philosophie de L’Algebre I. Paris : Presses Universitaires de France, 1962, p. 525.
- [67] Dantzig T. Number. The language of science. New York: The Free Press, 1967, p. 62.
- [68] Heinzmann G. Enter intuition et analyse. Poincaré et le concept de prédicativité. Paris: Blanchard, 1985, p. 26.
- [69] Lorenzen P. Methodisches Denken. Suhrkamp, 1968, p. 100.
- [70] Cantor G. Ueber eine elementare Frage der Mannigfaltigkeitslehre. Jahr.-buch Deut. Math.-Ver. 1 (1892) 75-78
- [71] Picker B. Mengenlehre I. Düsseldorf: 1973, p. 11.
- [72] Rucker R. Infinity and the mind. Princeton: Princeton Univ. Press, 1987, p. 252.
- [73] Zuckerman M.M. Sets and transfinite numbers. New York: Macmillan, 1973, p. 143.
- [74] Larsen M.D. Fundamental concepts of modern mathematics. Reading, MA: Addison-Wesley, 1970, p. 37.
- [75] Müller G.H. (Ed.) Sets and classes. On the work by Paul Bernays. Amsterdam: North-Holland, 1976, 18.
- [76] Fehr J. Introduction to the theory of sets. Englewood-Cliffs, NJ: Prentice-Hall, 1958, p. 18.
- [77] Bolzano B. Paradoxes of the infinite. London: Routledge & Kegan Paul, 1950, p. 96.
- [78] Gandy R.O. & Hyland J.M.E. (Eds.) Logic colloquium 76. Amsterdam: North-Holland, 1977, p. 169.
- [79] Cantor G. Ueber unendliche, lineare Punktmannigfaltichkeiten V. Math. Ann. 21 (1883) 545-586, see p. 578
- [80] Dotterer R.H. The definition of infinity. J. Philos. Psych. Sci. Meth. 15 (1918) 294-301
- [81] Hilbert D. Sur l’infini. Acta Math. 48 (1926) 91-122
- [82] Heyting A. Intuitionism. An introduction. Amsterdam: North-Holland, 1956, p. 32.
- [83] Zehna P.W. Sets with applications. Boston: Allyn & Bacon, 1966, p. 26ff.
- [84] Levy A. Axiom schemata of strong infinity in axiomatic set theory. Pac. J. Math. 10 (1960) 223-238
- [85] Levy A. Basic set theory. Mineola, NY: Dover, 2002, p. 78.
- [86] Hahn H. Infinity. [pp. 1593-1611 in: Newman J.R. (Ed.) The world of mathematics III. New York: Simon & Schuster, 1956].
- [87] Fang J. The illusory infinite. A theology of mathematics. Memphis, TN: Paideia Press, 1976, p. 169.
- [88] Dedekind R. Was sind und was sollen die Zahlen? Stetigkeit und irrazionale Zahlen. Braunschweig: 1969, pp. 1, 13ff.
- [89] Dedekind R. Essays in the theory of numbers. New York: Dover, 1963, pp. 11, 64.
- [90] Beth E.W. L’existence en mathématiques. Paris : 1956, p. 21.
- [91] Meschkowski H. Grundlagen der modernen Mathematik. Darmstadt, 1975, p. 159.
- [92] Brunschvicq L. Les étapes de la philosophie mathématique. Paris: A. Blanchard, 1972, p. 213.
- [93] Zippin L. Uses of infinity. New York: Random House, 1962, p. 24.
- [94] Olijnychenko P. On transfinite numbers and sets. London: 1976, p. 3.
- [95] Borel E. Les paradoxes de l’infini. Paris : Gallimard, 1946, p. 58.
- [96] Peano G. Selected works of Giuseppe Peano. London: Allen & Unwin, 1973, p. 67ff.
- [97] Fontenelle. Éléments de la géométrie de l’infini. Klincksieck: 1995, pp. 53, 211.
- [98] Blay M. Reasoning with infinite. From the closed world to mathematical universe. Chicago: The Univ. of Chicago Press, 1998, p. 137.
- [99] Finsler P. Über die Grundlegung der Mengenlehre II: Verteidigung. Comment. Math. 38 (1963) 172
- [100] Cusanus. De docta ignorantia. I.11.h 31 [in: Nikolaus von Kues. Philosophisch-theologische Werke. Lateinisch-Deutsch. Darmstadt: Wiss. Buchgesellschaft; excerpts in English are posted online on: http://www.sunysb.edu/philosophy/faculty/lmiller/DDI2.txt ] [101] Von Cues N. Vom Gottes sehen. Leipzig, 1944, p. 94.
- [101] Gminder A. Ebene Geometrie. München, 1932, p. 115.
- [102] Smith V.E. Philosophical physics. New York: Harper & Brothers, 1950, p. 132.
- [103] Brunner N. Dedekind-Endlichkeit und Wohlorderbarkeit. Mh. Math. 94 (1982) 9-31
- [104] Hadamard, Baire, Lebesgue, Borel. Cinq lettres sur la thèorie des ensembles. Bull. Soc. Math. France 33 (1905) 261
- [105] Gruender C.D. The Achilles paradox and transfinite numbers. Brit. J. Philos. Sci. 17 (1960) 219, see p. 228.
- [106] Ashtekar A. New perspectives in canonical gravity. Napoli: Bibliopolis, 1988, p. 3.
- [107] Dantzig T. Aspects of science. New York, 1937, p. 270.
- [108] Kharin N.N. Mathematical logic and set theory. RosWuzIzdat, 1963, p. 17 [in Russian].
- [109] Santayana G. The prestige of the infinite. J. Philos. 29 (1932) 281-289, see p. 284
- [110] Von Weizsäcker C.F. Aufbau der Physik. München: Carl Hanser Verlag, 1985, p. 362.
- [111] Ogilvy C.S. Excursions in geometry. New York: Oxford Univ. Press, 1969, p. 30.
- [112] Fraenkel A. Untersuchungen über die Grundlagen der Mengenlehre. Math. Z. 22 (1925) 250-273
- [113] Okumura H., Saitoh S. & Matsuura T. Relations of 0 and ∞. JTSS J. Tech. Soc. Sci. 1(1) (2017) 70-77 see p.74 on http://www.e-jikei.org/Journals/JTSS/issue/archives/vol01_no01/10_A020/Camera%20ready%20manuscript_JTSS_A020.pdf
- [114] Czajko J. On Conjugate Complex Time II: Equipotential Effect of Gravity Retrodicts Differential and Predicts Apparent Anomalous Rotation of the Sun. Chaos Solit. Fract. 11 (2000) 2001-2016 http://www.sciencedirect.com/science/article/pii/S0960077999000922
- [115] Czajko J. Galilei was wrong: Angular nonradial effects of radial gravity depend on density of matter. Int. Lett. Chem. Phys. Astron. 30 (2014) 89-105 https://www.scipress.com/ILCPA.30.89
- [116] Szekeres G. Effect of gravitation on frequency. Nature 220 (1968) 1116-1118.
- [117] Tricomi F.G. Integral equations. New York: Interscience, 1957, pp. 181, 184.
- [118] Longair M.S. Theoretical concepts in physics. An alternative view of theoretical reasoning in physics. Cambridge: Cambridge Univ. Press, 2006, pp. 421, 422.
- [119] Czajko J. Operational restrictions on morphing of quasi-geometric 4D physical spaces. Int. Lett. Chem. Phys. Astron. 41 (2015) 45-72 http://www.scipress.com/ILCPA.41.45.pdf
- [120] Czajko J. Operational constraints on dimension of space imply both spacetime and timespace. Int. Lett. Chem. Phys. Astron. 36 (2014) 220-235 http://www.scipress.com/ILCPA.36.220.pdf
- [121] Chevalley C. Fundamental concepts of algebra. New York: Academic Press, 1956, p. 125ff.
- [122] Witten E. Reflections on the fate of spacetime. Phys. Today April (1996) 24-30 http://www.sns.ias.edu/sites/default/files/Reflections(3).pdf
- [123] Boorse H.A. & Motz L. The world of the atom II. New York: Basic Books, 1966, p. 1224.
- [124] Needham T. Visual Complex Analysis. Oxford: Oxford Univ. Press, 2001, p. 314.
- [125] Banchoff T. & Lovett S. Differential geometry of curves and surfaces. Natick, MA: A.K. Peters, 2010, p. 192ff.
- [126] Jones G.A. & Singerman D. Complex functions. An algebraic and geometric viewpoint. Cambridge: Cambridge Univ. Press, 1987, p. 228f.
- [127] Hubbard B.B. The world according to wavelets. The story of a mathematical technique in the making. Wellesley, MA: A.K. Peters, 1998, pp. 53, 209.
- [128] Eisberg R.M. Time delay measurements. Rev. Mod. Phys. 36 (1964) 1100-1102
- [129] De Vasher K. Lightning from heaven. Video 1401: An enemy has done this. https://amazingdiscoveries.tv/media/1604/1401-an-enemy-has-done-this/ ; some videos on the site are provided also in several other languages.
- [130] God (The Inspirer). The Bible. Ephesians 6: 12 https://www.biblegateway.com/passage/?search=Ephesians+6:12&version=AKJV
- [131] Veith W. Clash of the minds: Righteousness by faith in verity pt. 2. Audio 263
- [132] https://amazingdiscoveries.tv/media/2252/263-righteousness-by-faith-in-verity-part-2/see minute ~34:20 and ~43:12.
- [133] White E.G. Patriarchs and prophets. Chapter 27: The law given to Israel. Audio: http://ellenwhiteaudio.org/patriarchs-and-prophets-white-estate/ see minute ~16:47; books are also available there.
Document Type
undetermined
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-16b8130e-2fe2-47d8-8e69-700654d52c35