Objects generated by an arbitrary natural number

Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367-8275
Volume 26, 2020, Number 4, Pages 57–62
DOI: 10.7546/nntdm.2020.26.4.57-62
Full paper (PDF, 156 Kb)

Details

Authors and affiliations

Krassimir Atanassov
1 Department of Bioinformatics and Mathematical Modelling,
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
2 Intelligent Systems Laboratory
Prof. Asen Zlatarov University, Bourgas-8000, Bulgaria

Abstract

The set \underline{Set}(n), generated by an arbitrary natural number n, is defined. Some arithmetic functions, defined over its elements are introduced. Some of the arithmetic, set-theoretical and algebraic properties of the new objects are studied.

Keywords

  • Algebraic objects
  • Arithmetic functions
  • Natural numbers
  • Sets

2010 Mathematics Subject Classification

  • 11A25

References

  1. Atanassov, K. (1985). Short proof of a hypothesis of A. Mullin. Bulletin of Number Theory and Related Topics, Vol. IX (2), 9–11.
  2. Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham.
  3. MacLane, S., & Birkhoff, G. (1967). Algebra, The Macmillan Co., New York.

Related papers

  1. Atanassov, K. (2022). Objects generated by an arbitrary natural number. Part 2: Modal aspect. Notes on Number Theory and Discrete Mathematics, 28(3), 558–563.
  2. Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect. Notes on Number Theory and Discrete Mathematics, 29(1), 171-180.
  3. Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 4: New aspects. Notes on Number Theory and Discrete Mathematics, 29(3), 589-597.
  4. Atanassov, K., & Sándor, J. (2023). On a modification of Set(n). Notes on Number Theory and Discrete Mathematics, 29(4), 813-819.
  5. Atanassov, K. T. (2024). On the set of Set(n)’s. Notes on Number Theory and Discrete Mathematics, 30(3), 590-594.

Cite this paper

Atanassov, K. (2020). Objects generated by an arbitrary natural number. Notes on Number Theory and Discrete Mathematics, 26 (4), 57-62, DOI: 10.7546/nntdm.2020.26.4.57-62.

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