Titlebook: Hypernumbers and Extrafunctions; Extending the Classi Mark Burgin Book 2012 Mark Burgin 2012 differentiation.extrafuntion.hypernumber.integ

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Hypernumbers and Extrafunctions978-1-4419-9875-0Series ISSN 2191-8198 Series E-ISSN 2191-8201

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Hypernumbers,In this chapter we introduce real hypernumbers and study their properties in Sect. 2.1. Algebraic properties are explored in Sect. 2.2, and topological properties are investigated in Sect. 2.3. In a similar way, it is possible to build complex hypernumbers and study their properties (Burgin 2002, 2004, 2010).

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Conclusion: New Opportunities,Many topics and results in the theory of hypernumbers and extrafunctions have been left beyond the scope of this little book as its goal is to give a succinct introduction into this rich and multilayered theory. Here we briefly describe some of these topics and results, articulating open problems and directions for further research.

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Mark BurginDesigned to introduce the reader to hypernumbers and extrafunctions, which is another rigorous mathematical approach to operations with infinite values.Shows that even in the most standard case of rea

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How to Differentiate Any Real Function,y of approximations are presented. We consider approximations of two types: approximations of a point by pairs of points, which are called A-approximations and used for differentiation, and approximations of topological spaces by their subspaces, which are called B-approximations and used for integration.

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