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.

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.

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.

编码方式采用实数编码；

Real number coding is adopted.