Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

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PARITY OF DYADIC RATIONALS AND SURREAL NUMBERS

Authors

  • J. A. Nieto
  • J. A. Escalante-Javalera
  • C. A. Somera-Patrón
  • E. J. Villaseñor-González

DOI:

https://doi.org/10.17654/0972087124010

Abstract

In this work, via the dyadic rational fractions, we establish a link between parity of rational numbers and surreal numbers. Our strategy for this goal is to apply the parity concept of rationals to the dyadic rational fractions derived from surreal number theory.

Received: February 4, 2024
Revised: April 19, 2024
Accepted: April 27, 2024

References

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P. Lynch and M. Mackey, Parity and Partition of the Rational Numbers; arXiv:2205.00565 [math.NT].

J. H. Conway, On Number and Games, A. K. Peters, 2nd ed., 2001.

D. E. Knuth, Surreal Numbers: How Two Ex-students Turned on to Pure Mathematics and Found total Happiness: A Mathematical Novelette, Addison-Wesley Publishing Co., 1974.

H. Gonshor, An introduction to the theory of surreal numbers, London Mathematical Society Lectures Notes Series, Vol. 110, Cambridge Univ. Press, 1986.

C. Tøndering, Surreal Numbers - An Introduction. URL:

http://www.tondering.dk/claus/surreal.html

C. Avalos-Ramos, J. A. Félix-Algandar and J. A. Nieto, Dyadic rationals and surreal number theory, IOSR Journal of Mathematics (IOSR-JM) 16 (2020), 35-43.

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L. Vepstas, The Minkowski question mark, and the modular group, (2004). https://www.academia.edu/3221306.

J. A. Nieto, Remarks on dyadic rationals and surreal numbers, UAS, 2023 (in preparation).

J. Ritter, Closing the eye of Horus: The rise and fall of ‘Horus-eye fractions’, John Steele and Annette Imhausen, eds., Under One Sky Publisher, Ugarit-Verlag, 2003.

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Published

2024-05-11

Issue

Vol. 141 No. 2 (2024)

Section

Articles

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How to Cite

PARITY OF DYADIC RATIONALS AND SURREAL NUMBERS. (2024). Far East Journal of Mathematical Sciences (FJMS), 141(2), 155-167. https://doi.org/10.17654/0972087124010