Constructive mathematics: left numbers and comparison

Yuhan Chen; Zixi Chen; Guoyi Jiang; Zeyang Zhang

doi:10.1117/12.2628176

22 April 2022 Constructive mathematics: left numbers and comparison

Yuhan Chen, Zixi Chen, Guoyi Jiang, Zeyang Zhang

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 1216342 (2022) https://doi.org/10.1117/12.2628176
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

Certain programs equipped with the second program which measures the convergence rate of the Cauchy sequence could produce a constructive real number. Therefore, one cannot determine the exact value of the limit, but instead make some estimations of the limit. In this paper, we first propose the concept of Left (L) numbers, and then prove two theorems associated with left numbers, even without the convergence regulator it might be non-existent. By definition, the L number could be compared using the symbol >, ≥, <, and ≤. The first result is that it is impossible to find the algorithm which for any L numbers a, b and a rational number q, determines if a≤ b + q or a ≥ b − q. The second one is that if given ¬(a > b) (a & b are Left numbers), we can say that a ≤ b is also true. And the methods that we will use are proof by contradictions and some figures.

Citation Download Citation

Yuhan Chen, Zixi Chen, Guoyi Jiang, and Zeyang Zhang "Constructive mathematics: left numbers and comparison", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 1216342 (22 April 2022); https://doi.org/10.1117/12.2628176

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