超限归纳法

利用超限归纳法，他们可继续下去。

They can continue by transfinite induction .

证明了一个适用于任意有序集的一般归纳原理，以此为基础导出了数学归纳法、超限归纳法和连续归纳法，从而揭示出三种归纳法的共同基础。

In this paper , a general inductive principle for any ordered set is proved , and the mathematical induction , the transfinite induction and the continual induction are then deduced .

文献〔1〕建立了Г－环M的QN－根.本文通过其它途径给出了该根另外二个等价性定义：（1）可用超限归纳法构造出QN－根；

The QN-radical of gamma ring M had been established in ( 1 ) .

依超限归纳法的定义

Definition by transfinite inductio

本文介绍了如何用超限归纳法来作出σ环的构造，以便证明测度论中的某些定理。

This piece describes how to work out the structure of the o-ring by using the transfinite induction , so that it is easier to prove some of the principles in the measure theory .