@MISC{BINARI_6.MIZ,
  AUTHOR = {Okazaki, Hiroyuki},
  TITLE = {Binary Representation of Natural Numbers},
  SECTION1 = {Preliminaries},
  SECTION2 = {Homomorphism from the Natural Numbers to the Bitstreams},
  SECTION3 = {Homomorphism from the Bitstreams to the Natural Numbers},
  DAY = {29},
  MONTH = {September},
  YEAR = {2018},
  ADDRESS1 = {Shinshu University, Nagano, Japan},
 SUMMARY = {Binary representation of integers and arithmetic operations
  on them have already been introduced
  in MML \cite{BINARITH.ABS,BINARI_2.ABS,BINARI_3.ABS,BINARI_4.ABS}.
  However, these articles formalize the notion of integers as mapped
  into a certain length tuple of boolean values.
  In this article, we formalize the binary representation of natural
  numbers which maps ${\mathbb N}$ into bitstreams.},
  ACKNOWLEDGEMENT = {This study was supported in part by JSPS KAKENHI Grant Numbers JP17K00182.
     The authors would also like to express our gratitude to
     Prof. Yasunari Shidama for his support and encouragement.}}


