Abstract
AbstractIn this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirahã, working with only three numerals (one, two, many) can help us to change our perception of these paradoxes. A recently introduced methodology allowing one to work with finite, infinite, and infinitesimal numbers in a unique computational framework not only theoretically but also numerically is briefly described. This methodology is actively used nowadays in numerous applications in pure and applied mathematics and computer science as well as in teaching. It is shown in the article that this methodology also allows one to consider the paradoxes listed above in a new constructive light.
Publisher
Springer Science and Business Media LLC
Reference67 articles.
1. Alexander, A.: Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Scientific American: Farrar, Straus and Giroux, New York (2014)
2. Amodio, P., Iavernaro, F., Mazzia, F., Mukhametzhanov, M.S., Sergeyev, Ya.D.: A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic. Math. Comput. Simul. 141, 24–39 (2017)
3. Antoniotti, L., Caldarola, F., d’Atri, G., Pellegrini, M.: New Approaches to Basic Calculus: An Experimentation Via Numerical Computation. Lecture Notes in Computer Science, vol. 11973, pp. 329–342 (2020)
4. Antoniotti, L., Caldarola, F., Maiolo, M.: Infinite numerical computing applied to Hilbert’s, Peano’s, and Moore’s curves. Mediterr. J. Math. 17(3), article number 99 (2020)
5. Butterworth, B., Reeve, R., Reynolds, F., Lloyd, D.: Numerical thought with and without words: evidence from indigenous Australian children. Proc. Natl. Acad. Sci. USA 105(35), 13179–13184 (2008)
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