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Some paradoxes of infinity revisited

Sergeyev, Yaroslav (2022) Some paradoxes of infinity revisited. Mediterranean Journal of Mathematics, 19 (143). pp. 1-28.

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Abstract

In 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, Pirah ̃a, 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.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Sergeyev, Yaroslavyaro@dimes.unical.it0000-0002-1429-069X
Keywords: Paradoxes of infinity, counting systems, Pirah˜a, Munduruk´u, grossone.
Subjects: Specific Sciences > Cognitive Science > Computation
Specific Sciences > Computation/Information
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Mathematics
Specific Sciences > Cognitive Science > Perception
Depositing User: Prof. Yaroslav Sergeyev
Date Deposited: 22 Sep 2024 18:19
Last Modified: 22 Sep 2024 18:19
Item ID: 23927
Journal or Publication Title: Mediterranean Journal of Mathematics
Publisher: Birkhauser
Official URL: https://link.springer.com/article/10.1007/s00009-0...
DOI or Unique Handle: 10.1007/s00009-022-02063-w
Subjects: Specific Sciences > Cognitive Science > Computation
Specific Sciences > Computation/Information
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Mathematics
Specific Sciences > Cognitive Science > Perception
Date: 2022
Page Range: pp. 1-28
Volume: 19
Number: 143
URI: https://philsci-archive.pitt.edu/id/eprint/23927

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