Relation
现代数学的很多概念都是建立在Set的基础之上，比如我们熟知的Function概念，Relation也是如此，维基百科中介绍Relation的是Finitary relation。
Definition of relation
关于relation的定义，在Discrete-math\Book-Discrete-Mathematics-and-Its-Applications\Chpater-9-Relations中给出了：
Relationships between elements of sets occur in many contexts. Every day we deal with relationships such as those between a business and its telephone number, an employee and his or her salary, a person and a relative, and so on. In mathematics we study relationships such as those between a positive integer and one that it divides, an integer and one that it is congruent to modulo 5, a real number and one that is larger than it, a real number
xand the valuef(x)wherefis a function, and so on. Relationships such as that between a program and a variable it uses, and that between a computer language and a valid statement in this language often arise in computer science.Relationships between elements of sets are represented using the structure called a relation, which is just as sub set of the Cartesian product of the sets. Relations can be used to solve problems such as determining which pairs of cities are linked by airline flights in a network, finding a viable order for the different phases of a complicated project, or producing a useful way to store information in computer databases.
Relationship和relation
需要区分清楚relationship和relation：
relationship：就是我们平时所说的“关系”，比如“大于”、“小于”
relation：它是discrete math中对relationship的表示，它是一个set，它包含所有的ordered-pair
严格来说，我们平时所说的“关系”应该使用“relationship”这个词语。
wikipedia Finitary relation
Finitary relation的含义是“有限元关系”，我们主要讨论的是Binary relation（二元关系）。
wikipedia Binary relation
In mathematics, a binary relation over two sets A and B is a set of ordered pairs (a, b), consisting of elements a of A and elements b of B. That is, it is a subset of the Cartesian product A × B. It encodes the information of relation: an element a is related to an element b, if and only if the pair (a, b) belongs to the set.
NOTE:
relation的本质上是set。
查看Binary relation和Function可知，Binary relation是一个比Function更加宽泛的概念：Function是一种Binary relation，但是反之则不一定成立。
关系的性质
Transitive relation
"transitive"的中文意思是“传递性”，transitive特性是一个非常优良的特性，它是很多**computation**的前提条件，下面会对此进行说明。
Transitivity is a key property of both partial orders and equivalence relations。
Application in computation
1) Order
要想进行排序，则关系必须具备transitive特性。
2) Rewrite（proof）
按照工程automata-and-formal-language中的思想，rewrite的过程其实就是“推导”的过程。
一个例子就是：
stock：证券、股票；
股票：A股、B股;
则stock：A股、B股。
3) Closure
参见Closures-of-relation
4) Recursive
具备传递性的relation，它的computation可以采用recursion：重复地应用这个relation。
具备传递性的relation，它所形成的结构往往具备递归性。
在Relation-structure-computation\Computation\index.md的“relation and recursion”章节，对这个问题进行了讨论。
Reflexive relation
“reflexive”即“反射性”。
Symmetric relation
“symmetric”即“对称”
Relational algebra
关系代数，这是DBMS的基础。
TO READ
wikipedia Hasse diagram