LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
dos Reis, Tiago S.; Anderson, James A.D.W. (2014)
Languages: English
Types: Unknown
Subjects:
A geometrical construction of the transcomplex numbers was given\ud elsewhere. Here we simplify the transcomplex plane and construct the\ud set of transcomplex numbers from the set of complex numbers. Thus\ud transcomplex numbers and their arithmetic arise as consequences of their\ud construction, not by an axiomatic development. This simplifes transcom-\ud plex arithmetic, compared to the previous treatment, but retains totality\ud so that every arithmetical operation can be applied to any transcomplex\ud number(s) such that the result is a transcomplex number. Our proof\ud establishes the consistency of transcomplex and transreal arithmetic and\ud establishes the expected containment relationships amongst transcomplex,\ud complex, transreal and real numbers. We discuss some of the advantages\ud the transarithmetics have over their partial counterparts.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] Simon L. Altmann. Rotations, Quaternions and Double Groups. Dover Publications Inc, 1986.
    • [2] J. A. D. W. Anderson. Representing geometrical knowledge. Phil. Trans. Roy. Soc. Lond. Series B., 352(1358):1129-1139, 1997.
    • [3] James A. D. W. Anderson. Exact numerical computation of the rational general linear transformations. In Longin Jan Lateki, David M. Mount, and Angela Y. Wu, editors, Vision Geometry XI, volume 4794 of Proceedings of SPIE, pages 22-28, 2002.
    • [4] James A. D. W. Anderson. Perspex machine xi: Topology of the transreal numbers. In S.I. Ao, Oscar Castillo, Craig Douglas, David Dagan Feng, and Jeong-A Lee, editors, IMECS 2008, pages 330-33, March 2008.
    • [5] James A. D. W. Anderson. Evolutionary and revolutionary effects of transcomputation. In 2nd IMA Conference on Mathematics in Defence. Institute of Mathematics and its Applications, Oct. 2011.
    • [6] James A. D. W. Anderson. Trans-floating-point arithmetic removes nine quadrillion redundancies from 64-bit ieee 754 floating-point arithmetic. In this present proceedings, 2014.
    • [7] James A. D. W. Anderson and Tiago S. dos Reis. Transreal limits expose category errors in ieee 754 floating-point arithmetic and in mathematics. In Submitted for consideration in this proceedings, 2014.
    • [8] James A. D. W. Anderson, Norbert Vo¨lker, and Andrew A. Adams. Perspex machine viii: Axioms of transreal arithmetic. In Longin Jan Lateki, David M. Mount, and Angela Y. Wu, editors, Vision Geometry XV, volume 6499 of Proceedings of SPIE, pages 2.1-2.12, 2007.
    • [9] James A.D.W. Anderson and Walter Gomide. Transreal arithmetic as a consistent basis for paraconsistent logics. This proceedings, 2014.
    • [10] Jesper Carlstr¨om. Wheels - on division by zero. Mathematical Structures in Computer Science, 14(1):143-184, 2004.
    • [11] Tiago S. dos Reis and James A. D. W. Anderson. Transdifferential and transintegral calculus. In In this proceedings, 2014.
    • [12] W. Gomide and T. S. dos Reis. Nu´meros transreais: Sobre a no¸ca˜o de distˆancia. Synesis - Universidade Cat´olica de Petr´opolis, 5(2):153-166, 2013.
    • [13] F. G. Greenleaf. Introduction to Complex Variables. W. B. Saunders Company, 1972.
    • [14] D. Hilbert and S. Cohn-Vossen. Geometry and the Imagination. Chelsea, New York, 1952.
    • [15] J. M. Howie. Complex Analysis. Springer, 2003.
    • [16] Saunders Maclane and Garrett Birkhoff. Algebra. Chelsea Pub, 1999 (first published 1967).
    • [17] Alberto A. Martinez. The Cult of Pythagoras: Math and Myths. University of Pittsburgh Press, 2012.
    • [18] C. Neumann. Vorlesungen u¨ber Riemann's Theorie der Abel'schen Integrale. Teubner, Leipzig, 1865.
  • Inferred research data

    The results below are discovered through our pilot algorithms. Let us know how we are doing!

    Title Trust
    61
    61%
  • Discovered through pilot similarity algorithms. Send us your feedback.

Share - Bookmark

Cite this article