它的“部分排序”是什么意思？和“总排序”；在讨论Lamport的同步算法？ [英] What does it mean by "partial ordering" and "total ordering" in the discussion of Lamport's synchronization Algorithm?
问题描述
我了解的是，部分排序和全部排序是两组规则。
What I understand is, partial ordering and total ordering are two sets of rules.
部分排序具有三个规则：
（1）如果a a b是同一过程中的两个事件，且a在b之前，则a-> b。
（2）...
（3）...
Partial ordering has Three rules:
(1) if a an b are two events in the same process and a comes before b, then a->b.
(2) ...
(3) ...
那么总订购额是多少？
为什么这样命名？
推荐答案
这些名称源于以下事实：在部分顺序中，并非所有元素都是可比的，而在总顺序中，所有元素都是可比的：
Those names stem form the fact that in a partial order not all elements are comparable while in a total order all elements are comparable:
集合元素的部分顺序由三个属性定义必须保留所有元素 a ， b 和 c ：
A partial order on the elements of a set is defined by three properties that have to hold for all elements a, b and c:
- Reflexivity:
a ≤ a - Antisymmetry: if
a ≤ bandb ≤ a, thena = b - Transitivity: if
a ≤ bandb ≤ c, thena ≤ c
此定义捕获排序事物的含义的直觉的实质是：每个事物与其自身的大小相同，可以比另一个事物小，但是另一个事物不比其自身小。最后，如果一件事物比另一事物小，比另一事物小，那么它也比第三事物小。
This definition capture the essence of the common intuition of what it means to order things: each thing is the same "size" as itself, it can be "smaller" than an other but then the other is not "smaller" than itself. Finally if a thing is "smaller" than an other, which is "smaller" than a third then it is also "smaller" than the third.
总订单是具有附加属性的部分订单：
A total order is a partial order with the additional property:
- < a href = https://en.wikipedia.org/wiki/Connex_relation rel = nofollow noreferrer>联系度：
a≤b或b≤a
- Connexity:
a ≤ borb ≤ a
此定义表示，总的来说，任何两件事都是可比的。以部分顺序排列的事物既不需要彼此较小，也不需要相反，总的来说，每个事物都可以彼此较小或较小。
This definition says that in a total order any two things are comparable. Wheras in a partial order a thing needs neither to be "smaller" than an other nor the other way around, in a total order each thing is either "smaller" than an other or the other way around.
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