最后证明了良序集和实数集合具有序拓扑遗传性。
Finally we prove that well-ordered set and real set both have ordered topological hereditary.
实数集的上确界公理用到了实数集的子集，这是一种二阶逻辑的陈述。
The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement.
模糊变量是描述模糊现象的数学方法，它被定义为一个从可能性空间到实数集的函数。
Fuzzy variables are mathematical descriptions for fuzzy phenomena, and are de-fined as functions from a possibility space to the set of real Numbers.
在前期工作的基础上，提出一个实数集（连续统）可数性的一个更严格、更直观的证明。
This paper gives a new proof of continuum's countability which is more strict and di-rectviewing on the basis of the earlier work.
现在检查第二个记录集，其中它的日期和事实数据会被添加到查询中。
Now examine this second record set in which date and fact data were added to the query.
我们正期待着在接下来的几个月里，看着它的性能随真实数据集的增加而增加，并看到我们其它的应用怎样从我们的经验中受益。
We are looking forward to watching its performance over the next few months with additional real-world datasets and seeing how our other applications can benefit from our experience.
他们认为“我们在真实数据集的测试结果表现这款软件非常有前途”。
文中将这两种方法进行了推广，给出了一系列负实数阶广义M集的内部结构图。
These two methods were extended, and a series of internal structure images of the general Mandelbrot sets for negative real index number were given out.
在该算法实现过程中，采用实数编码法进行编码，每个染色体代表一组描述协商方案的属性集。
In the implementation process of algorithm, a real number coding method was adopted with each chromosome representing an attribute set describing the negotiation project.
针对真实数据集进行的大量实验表明，该算法具有较高的效率，从而为多元形成性评价系统的成功应用奠定了基础。
A large number of experiments according to real data set; show that the algorithm has higher efficiency, which lays the foundation of the success of multiple formative assessment system.
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.
有一些R的子集很著名， 有一些的子集很著名，因为他们具有实数所不具备 的子集很著名 的特殊性质。在本节我们将讨论这样的子集，整数集 的特殊性质。
4-A Integers and rational numbers - There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers.
有一些R的子集很著名， 有一些的子集很著名，因为他们具有实数所不具备 的子集很著名 的特殊性质。在本节我们将讨论这样的子集，整数集 的特殊性质。
4-A Integers and rational numbers - There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers.
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