Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 35 No. 1 (2017): Revista Integración
Research and Innovation Articles

A coinductive approach to real analysis

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  • Guillermo Ortiz-Rico,
  • Lina Isabel Triviño-Viera
Guillermo Ortiz-Rico
Universidad del Valle, Departamento de Matemática, Cali, Colombia.
Lina Isabel Triviño-Viera
Universidad del Valle, Departamento de Matemática, Cali
DOI: https://doi.org/10.18273/revint.v35n1-2017007

Published 2017-08-09

Keywords

  • Categories,
  • Algebra,
  • Coalgebra,
  • Induction,
  • Coinduction

How to Cite

Ortiz-Rico, G., & Triviño-Viera, L. I. (2017). A coinductive approach to real analysis. Revista Integración, Temas De matemáticas, 35(1), 103–125. https://doi.org/10.18273/revint.v35n1-2017007

Abstract

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.

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