构造实数时常见的两种方法评注

A Commentary on Two Usual Methods of Constructing Real Numbers

按照数学分析的逻辑顺序,首先建立实数理论,在对极限运算完备的论域上发展极限方法,然后开展微积分的迎检工作.但作为基础的实数域的构造,直到19世纪后半叶才完成.本文从实数域的两种构造方法入手加以评注.

According to the logic order of mathematical analysis,a theory of real numbers should be established before limit process is operated in the field of the limit operation,and then the examination of calculus can be realized.However,it was not until the second half of the 19th century that the construction of the field of real numbers was accomplished.This paper makes a brief comment on the two methods of constructing the field of real numbers.