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  • Primitive Recursiveness of Real Numbers under Different Representations

    Author(s)
    Chen, Qingliang
    Su, Kaile
    Zheng, Xizhong
    Griffith University Author(s)
    Su, Kaile
    Year published
    2007
    Metadata
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    Abstract
    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 ...
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    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.
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    Journal Title
    Electronic Notes in Theoretical Computer Science
    Volume
    167
    DOI
    https://doi.org/10.1016/j.entcs.2006.08.018
    Subject
    Theory of computation
    Computational logic and formal languages
    Cognitive and computational psychology
    Publication URI
    http://hdl.handle.net/10072/57996
    Collection
    • Journal articles

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