离散数学与应用：集合论详解
本文详细探讨了集合论的基础定义，包括集合的性质、子集、空集、幂集和笛卡尔乘积。阐述了如何证明和反驳集合的属性，介绍了布尔代数的概念，并讨论了罗素悖论及其对集合定义的影响。此外，还涉及停机问题的思考。
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）
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