Construction of the Transreal Numbers from Hyperreal Numbers

Authors

  • Tiago Soares dos Reis Federal Institute of Education, Science and Technology of Rio de Janeiro

DOI:

https://doi.org/10.36285/tm.59

Abstract

We construct the transreal numbers and arithmetic from subsets of hyperreal numbers. In possession of this construction, we propose a contextual interpretation of the transreal arithmetical operations as vector transformations.

References

J.A.D.W. Anderson, N. Völker, and A.A. Adams, “Perspex Machine viii: Axioms of transreal arithmetic,” in Vision Geometry XV (L.J. Lateki, D.M. Mount, and A.Y. Wu, eds.), vol. 6499 of Proceedings of SPIE, pp. 2.1–2.12, 2007.

James A.D.W. Anderson and Tiago S. dos Reis. Construction of the transreal numbers from rational numbers via Dedekind cuts. Engineering Letters, 29(2): 477–492, 2021.

T.S. dos Reis. “Números transreais: matemática ou devaneio?” (Transreal numbers: mathematics or reverie?) Accessed on 30 April 2021. Lecture Notes in História da Ciência e da Tecnologia: 14◦ Seminário Nacional de História da Ciência e da Tecnologia 2014 (History of Science and Technology: 14th National Seminar of History of Science and Technology 2014).

T.S. dos Reis, W. Gomide, and J.A.D.W. Anderson. “Construction of the transreal numbers and algebraic transfields.” Accessed on 30 April 2021. International Journal of Applied Mathematics, 46(1), pp.11–23, 2016.

T.S. dos Reis and J.A.D.W. Anderson, “Construction of the transcomplex numbers from the complex numbers,” in Lecture Notes in Engineering and Computer Science: Proceedings of The World Congresson Engineering and Computer Science 2014, WCECS 2014, 22-24 O-tober, 2014, San Francisco, USA., vol. 1, pp. 97–102, 2014.

T.S. dos Reis and J.A.D.W. Anderson, “Transquaternions.” In preparation.

A. Robinson. Non-Standard Analysis. Princeton University Press,1996.

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Published

2021-07-04

How to Cite

Reis, T. S. dos. (2021). Construction of the Transreal Numbers from Hyperreal Numbers. Transmathematica. https://doi.org/10.36285/tm.59

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Primary Article