《Types and Programming Languages》的笔记-第18页
- 章节名：Ordered Sets
- 页码：第18页 2019-06-15 19:13:39
- A reflexive and transitive relation R on a set S is called a preorder on S.
- A reflexive, transitive, and anti-symmetric relation R is called a partial order on S.
- A reflexive, transitive, and symmetric relation on a set S is called an equivalence on S.
最小上确界，最大下确界 Suppose that ≤ is a partial order on a set S and s and t are elements of S. An element j 2 S is said to be a join (or least upper bound) of s and t if
- s≤j and t≤j, and
- for any element k ∈S with s≤k and t≤k, we have j≤k.
Similarly, an element m 2 S is said to be a meet (or greatest lower bound) of s and t if
- m ≤ s and m ≤ t, and
- for any element n ∈S with n ≤ s and n ≤ t, we have n ≤m.
良基关系 在数学中，类 X 上的一个二元关系 R 被称为是良基的，当且仅当所有 X 的非空子集都有一个 R-极小元
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