数学归纳法的逻辑正确性 Well-ordering principle of N. Every nonempty subset of the natural numbers contains a minimum. Proof.反证法 Suppose the induction principle were false.Then there would exist an assertion P that would satisfy conditions(i)and(i)of the the- 几个问题： orem,but P(n)would be false for some ne Z+.So let A=(k e 1.良序性如果没 Z:P(k)is false).Our supposition implies that A is nonempty.By 有，数学归纳法 the well-ordering principle [p.135],the set A has a minimum.Let 会出什么问题？ m denote this minimum.By condition(①，m≠l.Since m∈Z+,it follows that m >2.Consider the integer n =m-1 1.Since n m and m is the minimum of A,we know that n g A.Thus P(n)is true. By condition(i),P(n+1)is true too.But P(n+1)=P(m),so P(m) must also be true,a contradiction. ■数学归纳法的逻辑正确性 几个问题： 1.良序性如果没 有，数学归纳法 会出什么问题？ 反证法