通过完全由有理数构成的区间套来揭示无理数的存在

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

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继续

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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