"Philosophy of Mathematics and Mathematics Education". Peressini, Anthony Peressini, Dominic (2007).18 Unconventional Essays on the Nature of Mathematics. "Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics". Euclid in the Rainforest: Discovering Universal Truths in Logic and Math. To infinity and beyond: a cultural history of the infinite. The American Mathematical Monthly 79 (3): 242–251. The College Mathematics Journal 15 (4): 299–308. The American Mathematical Monthly 74 (6): 669–673. The American Mathematical Monthly 105 (7): 636–639. "Unique Developments in Non-Integer Bases". Komornik, Vilmos Loreti, Paola (1998).The American Mathematical Monthly 43 (10): 610–617. The Montana Mathematics Enthusiast 7 (1): 3–30. A Comprehensive Textbook of Classical Mathematics: A Contemporary Interpretation. The development of the foundations of mathematical analysis from Euler to Riemann. Understanding Infinity: The Mathematics of Infinite Processes. The College Mathematics Journal 26 (1): 11–15. John Hewlett and Francis Horner, English translators., ed. The American Mathematical Monthly 111 (5): 411–425. "Surprises from mathematics education research: Student (mis)use of mathematical definitions" (PDF). Edwards, Barbara Ward, Michael (May 2004).Educational Studies in Mathematics 60 (2): 253–266. "Some historical issues and paradoxes regarding the concept of infinity: an APOS analysis: part 2". Dubinsky, Ed Weller, Kirk McDonald, Michael Brown, Anne (2005).The American Mathematical Monthly 67 (9): 900–903. The University Arithmetic: Embracing the Science of Numbers, and Their Numerous Applications. Functions of one complex variable I (2e ed.). How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics. Merriam-Webster's Guide to Everyday Math: A Home and Business Reference. Australian Mathematics Teacher 60 (4): 7–9. = 1?: A Perennial Question and Number Sense". Computer Arithmetic and Enclosure Methods. Automatic differentiation as nonarchimedean analysis. Winning Ways for your Mathematical Plays. Chaos: An introduction to dynamical systems. Difficultas huius scepticismi superandi est materies plurium tractatuum institutionis mathematicae.īibliographia Nihilominus aliqui discipuli eam interrogant, reiiciunt, aut paradoxum putant. et 1 diu a mathematicis agnoscitur et pars est disciplinae mathematicae communis. ![]() par 1 intellegitur, sed in ceteris signum "0.999." significare potest numerum qui numerum infinitum 9 habet sed quantitate infinitesima ab 1 discrepat.Īequalitas 0.999. In plerisque talibus systematibus, 0.999. Nonnulla alia systemata numeralia, ut numeri hyperreales, vere infinitesimos praeter zerum continent. et 1 pertinet ad absentiam infinitesimorum praeter zerum in systemate numerorum realium, in analysi mathematica usitatissimo. Eadem res in omnibus basibus vel similibus numerorum realium repraesentationibus occurrit.Īequalitas 0.999. Repraesentatio quae terminatur plerumque alteri praeponitur, sed ambae sunt validae. Zero excepto, quisque numerus decimalis qui terminum (seu numerum infinitum 0 sequentium) habet, repraesentationem geminam habet in qua numero infinito 9 terminatur (exempli gratia, 8.32 = 8.31999.). Haec aequalitas, quamquam a populo aliquando ignorata, multis modis et variis gradibus rigoris demonstrata est. ![]() (numeris 9 ad infinitum iterantibus, aliter 0.9̅, 0.(9), 0.9̇ scriptus) idem est ac numerus realis unus (1).
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