关于域的非代数结构——序

A Non-Algebra Structure of Field-Order

介绍将序的概念如何引进到抽象域中及有序域的概念,证明了有序域的一些性质。类比于实数域,讨论了有序域的稠密性及实性。在定义了基本序列及其极限之后,为把实分析理论推广到有序域上创造了条件。文末介绍了有序域理论应用的一个著名例子,从而说明科学的抽象能够更系统、完整、本质地反映具体事物的客观规律。

The article introduces the notion of order into abstract field,at the same time establishes the notion called the ordered field and proves its some properties, the comparison of the ordered field with the field of real numbers will certainly deduce the density and real property of the ordered field. After the fundamental sequence and its limit are defined .broad prospect for the introduction of the real analysis into the ordered field will be opened up. In the end. the well-known example of application of the ordered field is quoted,so as to show the following argument:the method of scientific abstract can still more systematically. perfectly and intrinsically reflect objective laws in some concrete matters.