实数连续性的16个等价命题

Sixteen Equivalent Propositions of Real Number Continuity

以十进位小数表示为出发点,借助连续归纳法把实数连续性常用的7个等价命题扩充到16个等价命题,其中包括有界闭集上连续函数的三大性质,这充分显示了实数连续性在整个数学分析中的重要地位和作用.

This paper,starting from decimal number expressions,by using real number continuous induction,increases the common 7 equivalent propositions to 16 equivalent propositions,including three features of the continuous function in a bounded closed set,which illustrates the important position and role of real number continuity in the overall mathematics analysis.