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在数学分析中,关于实数系的连续性有多种表达方式,这是大家熟知的。本短文中,我们给出实数系连续性的一种表达式,供同行参考,也可作大学低年级学生的一个有趣的练习。定义设ζ是实数系R中闭区间(可以是无穷区间)组成的集合,如果可由条件 (ⅰ)ζ中区间两两相交; (ⅱ)ζ中至少有一个区间的右端点有限, 推得ζ中所有区间有非空交,我们就说ζ有二元交性质。定理下面的两个事实等价:
In mathematical analysis, there are many ways to express the continuity of real numbers, which is well known. In this short essay we give an expression of the continuity of real numbers for reference by peers and an interesting exercise for lower grade students in college. Definitions Let ζ be a set of real interval R closed intervals (which can be infinite intervals). If the interval can be two or two by condition (i), (ii) the right endpoint of at least one interval in ζ is finite. There are non-empty exchanges in all the intervals in China. Let us say that there is a binary exchange. The following two facts of the theorem are equivalent: