利用有理数对实数逼近的表示方式，给出黎曼函数处处不可导的一种证明，给出单位圆周上的有理点在单位圆上稠密的证明。

Rational number can approximate to real number, use the notation of approximate one can prove Riemann function isn t differentiable anywhere, that the Rational points are dense in unit circle.

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摘要利用有理数对实数逼近的表示方式，给出黎曼函数处处不可导的一种证明，给出单位圆周上的有理点在单位圆上稠密的证明。

Rational number can approximate to real number use the notation of approximate one can prove riemann function isn't differentiable anywhere that the rational points are dense in unit circle .

youdao

因此说有理数集是一个有序的域。 序公理 。 因此说有理数集是一个有序的域 。

For this reason, we say that the set of rational numbers is an ordered field.

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And that idea was, we make a guess in the middle, we test it so this is kind of a guess and check, and if the answer was too big, then we knew that we should be looking over here. If it was too small, we knew we should be looking over here, and then we would repeat.

这些有理数是有序排列的,然后我们的想法是,首先在中间取个数作为猜想数，然后对这个猜想数进行验证，如果由猜想数得到的答案太大,我们知道应该跳过，比猜想数大的那个区间，如果太小的话。

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