论文标题
有理数的均衡和分区
Parity and Partition of the Rational Numbers
论文作者
论文摘要
我们定义了从整数到理性数字的均等范围的扩展。找到了三个奇偶校验课程 - 甚至奇怪和“无”。使用2-ADIC估值，我们将理由分为具有丰富代数结构的亚组。自然密度提供了一种区分无数集合的大小的方法。 calkin-wilf树具有非常简单的平价模式，序列“奇数/无/偶”无限期重复。这种模式意味着三个平价类别在理性中具有相等的自然密度。船尾领的树也有类似的结果。
We define an extension of parity from the integers to the rational numbers. Three parity classes are found -- even, odd and `none'. Using the 2-adic valuation, we partition the rationals into subgroups with a rich algebraic structure. The natural density provides a means of distinguishing the sizes of countably infinite sets. The Calkin-Wilf tree has a remarkably simple parity pattern, with the sequence `odd/none/even' repeating indefinitely. This pattern means that the three parity classes have equal natural density in the rationals. A similar result holds for the Stern-Brocot tree.
