本讲的前提是：
For the time being, all quantities occurring are assumed to be rational numbers.
假设我们所知道的数只有有理数，还不知道无理数的存在。
这里说的null-sequence 是rational null-sequence ，定义如下
![ge_thumb[13]](https://images2015.cnblogs.com/blog/1039027/201610/1039027-20161019040104732-1860975201.png "ge_thumb[13]")
继续
![ge_thumb[10]](http://images2015.cnblogs.com/blog/1039027/201610/1039027-20161019040106201-328715739.png "ge_thumb[10]")
![ge_thumb[11]](http://images2015.cnblogs.com/blog/1039027/201610/1039027-20161019040109592-244479706.png "ge_thumb[11]")
![ge_thumb[12]](http://images2015.cnblogs.com/blog/1039027/201610/1039027-20161019040114467-1653021680.png "ge_thumb[12]")
the second class is empty的例子请看
https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers#Nested_intervals_theorem
的Nested intervals theorem部分