CAJ | 학술논문

数学归纳法是证明与自然数有关的数学命题的一种完全归纳法,由于数学命题有种种形式和多种不同的实际需要,应用数学归纳法时,也要做出相应的变化,由此得到数学归纳法的一些其他形式.常见的形式一般有四种：第一数学归纳法,第二数学归纳法,倒推数学归纳法,螺旋数学归纳法.再介绍两种形式：跳跃数学归纳法和二元数学归纳法.并由皮亚诺公理和最小数原理给以证明,每种形式分别给出例题,介绍他们的应用.
수학귀납법시증명여자연수유관적수학명제적일충완전귀납법,유우수학명제유충충형식화다충불동적실제수요,응용수학귀납법시,야요주출상응적변화,유차득도수학귀납법적일사기타형식.상견적형식일반유사충：제일수학귀납법,제이수학귀납법,도추수학귀납법,라선수학귀납법.재개소량충형식：도약수학귀납법화이원수학귀납법.병유피아낙공리화최소수원리급이증명,매충형식분별급출례제,개소타문적응용.
Mathematics inductive method is demonstrated with a natural number related to the mathematical proposition of a complete induction.Since mathematical proposition has a variety of forms and a various different practical needs,corresponding changes should also be made when using mathematics inductive method,resulting in some other forms of mathematical induction.There are four typical forms： the first mathematical induction,the second mathematical induction,backward induction method and helical mathematical induction.Besides,two other forms are introduced： jumping mathematical induction and binary mathematical induction,proved by the Peano axioms and minimum principle,each with an example.