Pure and Applied Mathematics Journal

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Refined Definitions in Real Numbers and Vectors and Proof of Field Theories

Received: 07 April 2015    Accepted: 14 April 2015    Published: 24 April 2015
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Abstract

A set of new and refined principles and definitions in Real Numbers and Vectors are presented. What is a Vector? What is the meaning of the Addition of two Vectors? What is a Real Number? What is the meaning of their signs? What is the meaning of the Addition of two Real Numbers? What is the Summation Principle in Addition Operation? What is the Cancellation Principle in Addition Operation? What is the Meaning of the Multiplication of two Real Numbers? Is Field Theory a law? Can it be proved? All these issues are addressed in this paper. With better pictures and graphical presentations, proof of Field Theories in Real Numbers and Vectors including Commutativity, Associativity and Distributivity are also proposed.

DOI 10.11648/j.pamj.20150403.13
Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3, June 2015)
Page(s) 75-79
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Vector, Real Number, Number Line, Number Vector, Number Plane, Number Space, Summation Principle, Cancellation Principle, Field Theory, Commutativity, Associativity, Distributivity

References
[1] Galbis, Antonio & Maestre, Manuel (2012). Vector Analysis Versus Vector Calculus. Springer. p. 12. ISBN 978-1-4614-2199-3.
[2] J.E. Marsden (1976). Vector Calculus. W. H. Freeman & Company. ISBN 0-7167-0462-5.
[3] http://en.wikipedia.org/wiki/Vector_calculus.
[4] Solomon Feferman, 1989, The Numbers Systems: Foundations of Algebra and Analysis, AMS Chelsea, ISBN 0-8218-2915-7.
[5] Howie, John M., Real Analysis, Springer, 2005, ISBN 1-85233-314-6.
[6] http://en.wikipedia.org/wiki/Real_number.
[7] Stewart, James B.; Redlin, Lothar; Watson, Saleem (2008). College Algebra (5th ed.). Brooks Cole. pp. 13–19. ISBN 0-495-56521-0.
[8] http://en.wikipedia.org/wiki/Number_line.
[9] http://en.wikipedia.org/wiki/Field_(mathematics)
[10] Jacobson, Nathan (2009), Basic algebra 1 (2nd ed.), Dover, ISBN 978-0-486-47189-1.
[11] http://en.wikipedia.org/wiki/Linear_algebra
[12] http://en.wikipedia.org/wiki/Vector_space
[13] Lang, Serge (1987), Linear algebra, Berlin, New York: Springer-Verlag, ISBN 978-0-387-96412-6.
Author Information
  • DaVinci International Academy, Los Angeles, USA

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  • APA Style

    Edward T. H. Wu. (2015). Refined Definitions in Real Numbers and Vectors and Proof of Field Theories. Pure and Applied Mathematics Journal, 4(3), 75-79. https://doi.org/10.11648/j.pamj.20150403.13

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    ACS Style

    Edward T. H. Wu. Refined Definitions in Real Numbers and Vectors and Proof of Field Theories. Pure Appl. Math. J. 2015, 4(3), 75-79. doi: 10.11648/j.pamj.20150403.13

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    AMA Style

    Edward T. H. Wu. Refined Definitions in Real Numbers and Vectors and Proof of Field Theories. Pure Appl Math J. 2015;4(3):75-79. doi: 10.11648/j.pamj.20150403.13

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  • @article{10.11648/j.pamj.20150403.13,
      author = {Edward T. H. Wu},
      title = {Refined Definitions in Real Numbers and Vectors and Proof of Field Theories},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {3},
      pages = {75-79},
      doi = {10.11648/j.pamj.20150403.13},
      url = {https://doi.org/10.11648/j.pamj.20150403.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20150403.13},
      abstract = {A set of new and refined principles and definitions in Real Numbers and Vectors are presented. What is a Vector? What is the meaning of the Addition of two Vectors? What is a Real Number? What is the meaning of their signs? What is the meaning of the Addition of two Real Numbers? What is the Summation Principle in Addition Operation? What is the Cancellation Principle in Addition Operation? What is the Meaning of the Multiplication of two Real Numbers? Is Field Theory a law? Can it be proved? All these issues are addressed in this paper. With better pictures and graphical presentations, proof of Field Theories in Real Numbers and Vectors including Commutativity, Associativity and Distributivity are also proposed.},
     year = {2015}
    }
    

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