Abstract
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem of counting the number of complete subsets of any given set. That is, given any interval of integers ℌ ≔ [1, N] and letting \({\cal C}(N)\) denotes the complete set counting function, we establish the lower bound \({\cal C}(N)\) ≫ N log N.
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References
Ferreirós and José, Labyrinth of thought: A history of set theory and its role in modern mathematics, Springer Science & Business Media, 2008.
M. B. Nathanson, Graduate texts in mathematics, New York, NY: Springer New York 2000.
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Agama, T. Complete Sets. Indian J Pure Appl Math 51, 817–824 (2020). https://doi.org/10.1007/s13226-020-0433-5
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DOI: https://doi.org/10.1007/s13226-020-0433-5