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Binary Enumerability of Real Numbers (Extended Abstract)

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Book cover Computing and Combinatorics (COCOON 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

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Abstract

A real number x is called binary enumerable, if there is an effective way to enumerate all “1”-positions in the binary expansion of x. If at most k corrections for any position are allowed in the above enumerations, then x is called binary k-enumerable. Furthermore, if the number of the corrections is bounded by some computable function, then x is called binary w-enumerable. This paper discusses some basic properties of binary enumerable real numbers. Especially, we show that there are two binary enumerable real numbers x and y such that their difference x − y is not binary w-enumerable (in fact we have shown that it is even of no “w-r.e. Turing degree”).

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Fern Universität Hagen, 58084, Hagen, Germany

    Xizhong Zheng

Authors
  1. Xizhong Zheng
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Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

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© 1999 Springer-Verlag Berlin Heidelberg

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Zheng, X. (1999). Binary Enumerability of Real Numbers (Extended Abstract). In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_30

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  • DOI: https://doi.org/10.1007/3-540-48686-0_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

  • eBook Packages: Springer Book Archive

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