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 .
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.
在数集的基础上，在整数域上建立了一个新的交换半群，并在有理数域、实数域和复数域上进行了推广；作为应用，讨论了其元素的表示形式。
Based on the number set, a new commutative semi-group is established in the integer number and extended in number fields of rational number, real number and the complex number.
算术整数，有理数，实数。
The mathematics of integers, rational Numbers, real Numbers.
不是有理数的实数被称为无理数。理数的实数被称为无理数。
为了去除数据采样中的不真实数据，根据未确知有理数理论提出了一种新的采样数据的滤波方法。
In order to get rid of the untruthful sampled data, a new method data filtering is put forward in accordance with the theory of unascertained rational number.
为了去除数据采样中的不真实数据，根据未确知有理数理论提出了一种新的采样数据的滤波方法。
In order to get rid of the untruthful sampled data, a new method data filtering is put forward in accordance with the theory of unascertained rational number.
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