Abstract
This paper presents the main steps in defining a Finitely Supported Mathematics by using sets with atoms. Such a mathematics generalizes the classical Zermelo-Fraenkel mathematics, and represents an appropriate framework to work with (infinite) structures in terms of finitely supported objects. We focus on the techniques of translating the Zermelo-Fraenkel results into this Finitely Supported Mathematics over infinite (possibly non-countable) sets with atoms. Two general methods of proving the finite support property for certain algebraic structures are presented. Finally, we provide a survey on the applications of the Finitely Supported Mathematics in experimental sciences.
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Notes
- 1.
A multiset on an alphabet \(\varSigma \) is a function from \(\varSigma \) to \(\mathbb {N}\) where each element in \(\varSigma \) has associated its multiplicity.
- 2.
Let P be a predicate on A. We say that if P(a) is true for all but finitely many elements of A.
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Alexandru, A., Ciobanu, G. (2016). Main Steps in Defining Finitely Supported Mathematics. In: Yakovyna, V., Mayr, H., Nikitchenko, M., Zholtkevych, G., Spivakovsky, A., Batsakis, S. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2015. Communications in Computer and Information Science, vol 594. Springer, Cham. https://doi.org/10.1007/978-3-319-30246-1_5
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