1. ## 全序关系_百度百科

https://baike.baidu.com/item/全序

在数学中，集合 X 上的全序关系（Total order），简称全序、又名线性序（linear order）、简单序（simple order），或（非严格）排序（(non-strict) ordering），是在 X 上的反对称的、传递的和完全的任何二元关系。

2. ## Total order - Wikipedia

https://en.wikipedia.org/wiki/Total_order

In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set, which satisfies the following for all , and in : ().If and then (); If and then = (antisymmetric); or (strongly connected, formerly called total).; Total orders are sometimes also called simple, connex, or full orders.

3. ## 全序关系(Total Order)与偏序关系_winbobob的专栏-CSDN博客

https://blog.csdn.net/winbobob/article/details/37508073

全序关系（total order relation）及全序集（total order set，线序集或链）的定义 4. 全序关系的哈斯图 5. 良序关系（well order relation）及良序集（well order set）的定义 ... UA MATH523A 实分析1 集合论基础2 序关系与Zorn引理 一个不愿透露姓名的博客 ...

https://www.cnblogs.com/datacloud/p/3586761.html

4.2.2 总排序（Total order sorting） 有的时候需要将作业的的所有输出进行总排序，使各个输出之间的结果是有序的。有以下实例： 如果要得到某个网站中最受欢迎的网址（URL），就需要根据某种受欢迎的指标来对网址进行排序。

5. ## Totally Ordered Set -- from Wolfram MathWorld

mathworld.wolfram.com/TotallyOrderedSet.html

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial order plus an additional condition known as the comparability condition. A relation <= is a total order on a set S ("<= totally orders S") if the following properties hold. 1.

6. ## total order in nLab

https://ncatlab.org/nlab/show/total+order

A total order on a set is a way of ordering its elements to say that some elements precede others, with the understanding that any two elements can be compared one way or the other. Definitions. Given a set S S, a total order on S S is a (binary) relation ≤ \leq with the following properties: reflexivity: for any element x x of S S, x ≤ x x ...

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8. ## elementary set theory - what is total order - explanation…

https://math.stackexchange.com/questions/239118

The usual order ≤ on R is a linear (or total) order: if x, y ∈ R are any real numbers, either x ≤ y, or y ≤ x. To put it another way, if x and y are any real numbers, at least one of the statements x ≤ y and x ≥ y must be true. Contrast that with subsets of N. If A and B are subsets of N, it’s not the case that at least one of A ...

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