Constructive analysis of bishop and its comparison with classical analysis

Document Type : Research Paper

Authors

Yasouj University

Abstract

In this article, the intuitionistic logic of Brouwer in mathematics and the constructive analysis of Bishop is introduced based on this logic, and the differences with classical mathematical logic and analysis are explained. The fundamental difference in constructive analysis compared to classical analysis is that in constructive analysis, a solution and algorithm for finding desirable elements in existential theorems are always provided. Therefore, this type of mathematical analysis can be considered a very high-level programming language. To become familiar with the constructive reasoning methods, we first construct the system of real numbers using a constructive method and explain the fundamental differences of constructive analysis compared to classical analysis, which has its roots in the recognized properties of real numbers. Next, we present some existential theorems in classical analysis and their constructive equivalents. It will be seen that in most cases, exact existential theorems in classical analysis are transformed into approximate existential theorems in constructive analysis.

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References

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Mathematics and Society
Volume 3, Issue 3
September 2018
Pages 79-89

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History

  • Receive Date: 15 April 2018
  • Revise Date: 06 August 2018
  • Accept Date: 29 September 2018
  • Publish Date: 22 November 2018

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