Set

Tuple 元组

Definition: Are finite ordered list of elements

有限且有序的元素列表

Set 集合

Definition: are (unordered) collections of objects called elements or members of the set

Set is unordered and no duplicate.

Set cardinality 基数

Definition: is the number of elements of a set S, denoted |S|

集合中元素的数量，不包括空集。

Relation between two set

A=B：A is equal to B if A and B have the same elements

A和B相等就是A和B有相同的元素

A is disjoint from B if and only if there is no element that is in both A and B.

A与B不相交就是没有元素同时在A和B中

A⊆B: A is a subset of B if and only if every element in A is in B

A 是 B的子集，当且仅当A中所有的元素都在B中

A⊂B: A is a proper subset of B if and only if A is a subset of B but B is not a subset of A.

proper subset ：真子集

Unary Set Operations 一元集合操作

Powset() 幂集

Definition: is the set of all subsets of A

Complement 补集

Definition: is the difference between the universal set and A

Universal：全集

Binary set operations 二元集合操作

Union 并集

Definition: include all elements in A or in B or in A and B

intersection 交集

Definition: all elements that are in A and in B

Difference

Definition:all elements that are in A but not
in B

Cartesian product

Definition:AXB is the set whose members are all possible ordered pairs (a, b) where a is a member of A and b is a member of B

有序对