Correspondence Between Constructive Real Numbers and L Number in Constructive Mathematics

DOI

10.2991/assehr.k.211209.362How to use a DOI?

Keywords

Specker sequence; constructive mathematics; Specker Sequence

Abstract

In a broad sense, construction real number is a constructable real number, relative to the set of some construction methods. This essay mainly focuses on the left numbers in constructive analysis. After introducing the basic context and conditions in Constructive Mathematics, connections between concepts are put into consideration and discovered with reference. Specific propositions are also discussed and utilized to simplify and prove the statements listed below. It is deduced that in the context of constructive mathematics, there exists an algorithm such that given any constructive real number, it produces the corresponding Left (L) number, given the presumption that with equivalent constructive real numbers (CRN), equivalent Left numbers can be the output. In addition, the Specker sequence is utilized to prove that the converse statement is false. It is hoped that the paper can introduce more people to basic concepts and application of theorems in analysis.

Copyright

© 2021 The Authors. Published by Atlantis Press International B.V.

Open Access

This is an open access article under the CC BY-NC license.

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TY  - CONF
AU  - Xin Shen
AU  - Yiding Huang
AU  - Shixiang Wang
PY  - 2021
DA  - 2021/12/15
TI  - Correspondence Between Constructive Real Numbers and L Number in Constructive Mathematics
BT  - Proceedings of the 2021 3rd International Conference on Economic Management and Cultural Industry (ICEMCI 2021)
PB  - Atlantis Press
SP  - 2209
EP  - 2212
SN  - 2352-5428
UR  - https://doi.org/10.2991/assehr.k.211209.362
DO  - 10.2991/assehr.k.211209.362
ID  - Shen2021
ER  -