论文部分内容阅读
使用数学归纳法证明与自然数有关的命题,最为关键的一处是发现由k→k+l的关系。具体实施数学归纳法时,思维习惯总是遵循由k→k+l去探索。笔者常常在解题教学中,教导学生在正向探求受阻时,就超越传统思维习惯的束缚,打破常规,由k+l→k反推,透视问题的表象,从更深层次去揭示问题的本质。这种反推的思维对象,对数学归纳法的成功与失败,具有特别的意义。这里选例几个范例,共尝从k+l→k反推之乐趣。
Using mathematical induction to prove propositions related to natural numbers, the most critical one is to find the relationship from k → k + l. In the specific implementation of mathematical induction, the habit of thinking is always followed by k → k + l to explore. In the problem-solving teaching, the author often teaches students to go beyond the shackles of traditional habits of thinking when they are seeking to find their way forward, break the convention, push k+l→k to reverse the perspective of the problem, and reveal the essence of the problem from a deeper level. . This counter-reported thinking object is of special significance to the success and failure of mathematical induction. Here are a few examples of selected examples that share the fun of pushing back from k+l→k.