再论实数连续性的等价命题

The equal proposition of the Continuation of a real number

数学分析中描述实数连续性的六个等价命题是互为可推的,用任何一个命题都可以推出其它诸命题。通过给出的新命题:如果M是由[a,b]的闭子区间组成的一个局部的,可加的集族,则[a,b]∈M。并用它来证明闭区间上连续函数的性质更为优越。

in the mathematical analysis,the six equal propositions.Which are used to describe the continuation of the real number,can be mutually deduced. we may conclude all.other.various propositions with any of them.in this paper,a new proposition is assumed to prove the superiority of the nature of the continuous function on the closed interval.