数学归纳法的几个推广

Several generalizations of mathematical induction

将通常适用于自然数系的数学归纳法推广到了下有界整数集{n|n∈Z,n≥n0}与上有界整数集{n|n∈Z,n≤m0}及全体整数集Z.并证明了关于命题{P(m,n)}m,n∈Z的二元数学归纳法.

The usual induction is extended to lowerbounded integer set {n|n∈Z,n≥n0}, upperbounded integer set {n|n∈Z,n≤m0} and the integer set Z.As a consequence,an induction about the twovariable proposition {P(m,n)}m,n∈Z is given.