集合与图

Sets and Graphs

集合论是研究集合的数学理论,也是整个现代数学的基础。集合是集合论中最基本的对象。从集合的概念出发,描述集合论悖论的产生及解决方法,继而将集合区分为良基集和非良基集,探讨了用图来刻画集合的方法。考察集合和图的关系是探究非良基现象的一种有力工具,具有重要的理论意义。

Set theory is a mathematical theory in research of sets,also is the base of whole modern mathe-matics.In set theory,the set is the most basic object.Starting from the concept of sets,this paper described the production and solutions of set theory paradox and distinguished between well-founded sets and non-well-founded sets. Finally,we also discussed the method of picturing sets.Studying the relationship be-tween sets and their graphs is a powerful tool for exploring the phenomenon of non-well-foundation. It has an important theoretical significance.