实变函数教学中基数概念的直观化

Intuitive Teaching on the Concept of Cardinal Number in Real Function Theory

基数的概念、可列集的讨论,都可采用一一对应的方法使其既直观又容易理解,该思想可以证明2个集合是否对等,从而判定基数是否相同,借助于基数可以将集合进行分类,从而使无穷集合也有大小之分。以此为基点。

Adopting one to one correspondence makes it intuitive and easy to understand the concept of cardinal number and countable set.This method can prove whether two sets are reciprocal,whether their cardinal numbers are identical or not.Then all sets can be classified by means of cardinal number,while the size of infinite sets can also be calculated thereby.Based on this idea,some brand-new interpretation of the related results are given.