Chapter5 SET THEORY
5.1 Basic Definitions of Set Theory
The axiom of extension says that a set is completely determined by its elements; the order in which the elements are listed is irrevlevant, as is the fact that some elments may be listed more than once.
The def of set:
{a, b, c} {a, b}
A = {x in S| p(x)}
Subsets
Proper Subset(真子集)
Venne Diagram to presents the relationship between sets
Set Equality
Operations on Sets
A certain situation all sets being considered might be sets of real numbers. In such a situation, the set of real numbers would be called a universal set (全集)or auniverse of discourse for the discussion.
The Empty Set
Partitions of Sets
Mutually disjoint(互不相交)
Power Sets (幂集)
Cartesian Products(笛卡尔乘积)