关于实数的连续归纳法类似于数学归纳法,它与Dedekind公理等价。基于现有的研究成果,本文给出了连续归纳法的一个新的较为简单的证明方法；举例说明了连续归纳法的广泛应用,同时也为分析推理的机械化作了一些准备。

The continual induction for the real number is very similar to the mathematical induction for the natural number, the induction is equivalent to the Dedekind axiom, and could be widely used in the calculus research. Firstly, a novel proof for the continual induction is presented; the proof is more acceptable than the former. And then, some discussions on its applications are made, it gives some meaningful advices to the higher mathematics teaching. The continual induction could also be used in the mechanization research on analytical reasoning.