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.

中文翻译：

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成套

在本文中，我们介绍了集合完整性的概念。我们在整数集上研究此属性。当我们执行与集合兼容的各种操作时，我们将研究如何保留此属性。我们还介绍了对任何给定集合的完整子集进行计数的问题。也就是说，给定整数ℌ [1，N ]的任何间隔，并让\（{\ cal C}（N）\）表示完整的计数函数，我们建立下界\（{\ cal C}（N ）\） » ñ日志ñ。