The nonexistence of a constructive real number ordering algorithm

Jeff Xiangling Duan

doi:10.1117/12.2685945

28 July 2023 The nonexistence of a constructive real number ordering algorithm

Jeff Xiangling Duan

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275646 (2023) https://doi.org/10.1117/12.2685945
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

Constructive mathematics views traditional mathematics through the lens of computer algorithms. Namely, this study considers Constructive Real Numbers (CRNs), numbers that some computer programs may generate, and seeks to answer whether there exists a program that may sort any finite general set of CRNs into increasing order. The foundations of Computability Theory are introduced to be employed further in the study. Equipped with these tools, various propositions for the possibility of ordering CRNs are discussed and proven. Furthermore, we then use similar techniques to prove that, given a quadratic polynomial with CRN coefficients, there does not exist an algorithm that can always determine its number of roots.

Citation Download Citation

Jeff Xiangling Duan "The nonexistence of a constructive real number ordering algorithm", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275646 (28 July 2023); https://doi.org/10.1117/12.2685945

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