Scientific Research

An Academic Publisher

Representations of Each Number Type That Differ by Scale Factors ()

For each type of number, structures that differ by arbitrary scaling factors and are isomorphic to one another are described. The scaling of number values in one structure, relative to the values in another structure, must be compensated for by scaling of the basic operations and relations (if any) in the structure. The scaling must be such that one structure satisfies the relevant number type axioms if and only if the other structure does.

Keywords

Share and Cite:

P. Benioff, "Representations of Each Number Type That Differ by Scale Factors,"

*Advances in Pure Mathematics*, Vol. 3 No. 4, 2013, pp. 394-404. doi: 10.4236/apm.2013.34057.Conflicts of Interest

The authors declare no conflicts of interest.

[1] | P. Benioff, “New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems,” International Journal of Theoretical Physics, Vol. 50, No. 6, 2011, pp. 1887-1907. doi:10.1007/s10773-011-0704-3 |

[2] | P. Benioff, “Effects on Quantum Physics of the Local Availability of Mathematics and Space Time Dependent Scaling Factors for Number Systems,” In: I. Ion Cotaescu, Ed., Advances in Quantum Theory, InTech, 2012. http://www.intechopen.com/ doi:10.5772/36485 |

[3] | J. Barwise, “An Introduction to First Order Logic,” In: J. Barwise, Ed., Handbook of Mathematical Logic, North-Holland Publishing Co., New York, 1977, pp. 5-46. doi:10.1016/S0049-237X(08)71097-8 |

[4] | H. J. Keisler, “Fundamentals of Model Theory,” In: J. Barwise, Ed., Handbook of Mathematical Logic, North-Holland Publishing Co., New York, 1977, pp. 47-104. doi:10.1016/S0049-237X(08)71098-X |

[5] | R. Kaye, “Models of Peano Arithmetic,” Clarendon Press, Oxford, 1991, pp. 16-21. |

[6] | Wikipedia: Integral Domain. |

[7] | A. J. Weir, “Lebesgue Integration and Measure,” Cambridge University Press, New York, 1973, p. 12. |

[8] | J. Randolph, “Basic Real and Abstract Analysis,” Academic Press, Inc., New York, 1968, p. 26. |

[9] | J. Shoenfield, “Mathematical Logic,” Addison Weseley Publishing Co. Inc., Reading, 1967, p. 86. |

[10] | Wikipedia: Complex Conjugate. |

[11] | R. Smullyan, “Goel’s Incompleteness Theorems,” Oxford University Press,, New York, 1992, p. 29. |

[12] | S. Lang, “Algebra,” 3rd Edition, Addison Weseley Publishing Co., Reading, 1993, p. 272. |

[13] | I. Adamson, “Introduction to Field Theory,” 2nd Edition, Cambridge University Press, New York, 1982, Chapter 1. |

[14] | W. Rudin, “Principles of Mathematical Analysis,” 3rd Edition, International Series in Pure and Applied Mathematics, McGraw Hill Book Co., New York, 1976, p. 172. |

[15] | G. Mack, “Physical Principles, Geometric Aspects, and Locality Properties of Gauge Field Theories,” Fortshritte der Physik, Vol. 29, No. 4, 1981, pp. 135-185. doi:10.1002/prop.19810290402 |

[16] | I. Montvay and G. Münster, “Quantum Fields on a Lattice,” Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1994. doi:10.1017/CBO9780511470783 |

[17] | C. N. Yang and R. L. Mills, “Conservation of Isotopic Spin and Isotopic Gauge Invariance,” Physical Review, Vol. 96, No. 1, 1954, pp. 191-195. doi:10.1103/PhysRev.96.191 |

[18] | P. Benioff, “Towards a Coherent Theory of Physics and Mathematics,” Foundations of Physics, Vol. 32, No. 7, 2002, pp. 989-1029. doi:10.1023/A:1016561108807 |

[19] | P. Benioff, “Towards a Coherent Cheory of Physics and Mathematics: The Theory-Experiment Connection,” Foundations of Physics, Vol. 35, No. 11, 2005, pp. 1825-1856. doi:10.1007/s10701-005-7351-6 |

Copyright © 2020 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.