Which Numbers Simplify Your Problem?

Paolo Giordano ()
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Paolo Giordano: University of Vienna, Fakultät für Mathematik

A chapter in Mathematics Without Boundaries, 2014, pp 181-220 from Springer

Abstract: Abstract An extension of the ring of scalar quantities, from the usual field of real numbers to a non-Archimedean, sometimes permits to simplify some problems which, at a first sight, may seem not correlated with infinitesimal and infinite numbers. We present four simple cases, each one at the level of possibility for the creativity of a motivated student. The ring of Fermat reals and its applications to physics and differential geometry, the ring of Colombeau generalized numbers and its applications to the foundations of generalized functions, the Levi-Civita field and the derivation of complicated computer functions and the Surreals numbers as a universal non-Archimedean ring. The definition of each one of these rings is strongly motivated at elementary level and some open problems and ideas are introduced in the first two cases.

Keywords: Non-Archimedean rings; Infinitesimal numbers; Infinite numbers; Fermat reals; Colombeau generalized numbers; Levi-Civita field; Surreal numbers (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1106-6_7

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DOI: 10.1007/978-1-4939-1106-6_7

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