Abstract

ORTIZ-RICO, Guillermo  and  TRIVINO-VIERA, Lina Isabel. A coinductive approach to real analysis. Integración - UIS [online]. 2017, vol.35, n.1, pp.103-125. ISSN 0120-419X.  https://doi.org/10.18273/revint.v35n1-2017007.

Coinduction is a dual concept to induction; it has been discovered and studied recently. A simple way to understand its naturalness is noting that it refers to the largest fixed points, while induction refers to smallest fixed points. Originally the technical support of the coinduction was the lattices theory through the largest fixed points; now this support is in the language categories through the final F -coalgebras. The F -coalgebras is a dual concept of generalization to algebras for a functor F. In this paper we focus on a particular type of F-coalgebras: stream automata. Our aim will be to use the framework of stream automata to illustrate the coinductive character of real analysis through classical results as the fundamental theorem of calculus, Taylor series and the solution of certain differential equations.

Keywords : Categories; Algebra; Coalgebra; Induction; Coinduction.

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