论文标题
可数集的大多数交流
Most-Intersection of Countable Sets
论文作者
论文摘要
我们通过可计数集的自然密度“大多数”介绍了一个名为“大多数交流”的新型设置交流运算符，称为“大多数交流”，可用于确定给定的可计数（可能是无限）系统集合的多数特征。新操作员根据自然密度确定给定集合中“大多数”集中的元素。这个概念允许在统计集合中使用时，与标准交叉点运算符相比，与标准交叉点运算符相比，无限/有限收集的多数设置会员特征的大多数设置会员特征。我们还为形式的语言理论和超图提供了最多的交流操作员的一些应用。引入最多的交流操作员会导致纯数学和应用数学中的大量应用，其中一些我们愿意进行进一步研究。
We introduce a novel set-intersection operator called `most-intersection' based on the logical quantifier `most', via natural density of countable sets, to be used in determining the majority characteristic of a given countable (possibly infinite) collection of systems. The new operator determines, based on the natural density, the elements which are in `most' sets in a given collection. This notion allows one to define a majority set-membership characteristic of an infinite/finite collection with minimal information loss, compared to the standard intersection operator, when used in statistical ensembles. We also give some applications of the most-intersection operator in formal language theory and hypergraphs. The introduction of the most-intersection operator leads to a large number of applications in pure and applied mathematics some of which we leave open for further study.
