Primitive Recursiveness of Real Numbers under Different Representations
Author(s)
Chen, Qingliang
Su, Kaile
Zheng, Xizhong
Griffith University Author(s)
Year published
2007
Metadata
Show full item recordAbstract
In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure-Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computability of real numbers. However, the primitive recursive (p.r., for short) versions of these representations can lead to different notions of p.r. real numbers. Several interesting results about p.r. real numbers can be found in literatures. In this paper we summarize the known results about ...
View more >In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure-Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computability of real numbers. However, the primitive recursive (p.r., for short) versions of these representations can lead to different notions of p.r. real numbers. Several interesting results about p.r. real numbers can be found in literatures. In this paper we summarize the known results about the primitive recursiveness of real numbers for different representations as well as show some new relationships. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers.
View less >
View more >In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure-Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computability of real numbers. However, the primitive recursive (p.r., for short) versions of these representations can lead to different notions of p.r. real numbers. Several interesting results about p.r. real numbers can be found in literatures. In this paper we summarize the known results about the primitive recursiveness of real numbers for different representations as well as show some new relationships. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers.
View less >
Journal Title
Electronic Notes in Theoretical Computer Science
Volume
167
Subject
Theory of computation
Computational logic and formal languages
Cognitive and computational psychology