Well-order
在阅读维基百科Recursive definition的Form of recursive definitions章节时,发现了这个概念,遂对它进行了整理。
维基百科Well-order
笔记
Well-order VS total order
原文对Well-order 的定义如下:
In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.
显然,它是在 total order 的基础上添加了一个限制,那这限制有何意义呢?是保证S
的每个子集依然满足 total order?
其实理解well order的一个很好的方法是结合实例来进行理解,set theory所描述的tree就是一个典型的well order,在维基百科Tree (set theory):
In set theory, a tree is a partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. Frequently trees are assumed to have only one root (i.e. minimal element), as the typical questions investigated in this field are easily reduced to questions about single-rooted trees.
维基百科Well-founded relation
并没有理解维基百科Well-founded relation。