这个视频是上个视频关于数字系统大小的延续,其中讨论了自然数、整数和有理数的基数。这里讨论了无理数的基数性,并使用Cantor的对角论证,说明了无理数(因此是实数)如何多于自然数。
*这个话题一般不包括在BC高中的数学课程中,但是对于那些对数字系统感兴趣的人来说是非常有趣的。
This video is a continuation of the last video on the size of number systems, where the cardinalities of the naturals, wholes, integers and rationals were discussed. Here the cardinality of the irrationals are discussed, and using Cantor’s Diagonal argument, I show how there are more irrationals (and hence reals) than there are naturals. *This topic generally not covered in BC High school math curriculum, but is quite fascinating to those who are interested in number systems.