1)  mathematical induction

1.
Inclusion and exclusion principle proved with mathematical induction;

2.
Application of Mathematical Induction to the Mathematical Programming

3.
This paper pre-sented two general expressions and the property of generalized Fibonacci sequence Rn+1=uRn+vRn-1,R0=a,R1=b by using the mathematical induction method and seeking the root of characteristic equation.

2)  induction [英][ɪn'dʌkʃn]  [美][ɪn'dʌkʃən]

1.
The Error-Analysis and Teaching Strategy in Teaching Induction for Senior High School Students;

2.
In this paper, by using the method of analogue to treat a special determinant, we come to a general conclusion, which has been proved correct by induction.

3)  mathematic induction

1.
Based on analysis of a typical case in teaching course of recursion,the thesis explains recursion through mathematic induction,the new way of teaching produces a good effect.

2.
With the use of the minimum nature the paper comments the reasonableness and the mutual relation of dependence in Condition one and Two of mathematic induction.

4)  inductive method

1.
Two notes about changes of inductive method;

2.
This thesis talks about the proving steps and every variety of form of inductive method.

5)  mathematics induction

1.
By skillfully using mathematics induction and interchanging-colors, this article successfully solves the simplifying prohlem advanced by A.

2.
We use mathematics induction to show them.

3.
Some examples of mathematics induction are presented here which we used in teaching practice.

6)  generallzed mathematical induction method

 数学归纳法mathematical induction   适用于论证与所有自然数有关的命题的归纳方法。与所有自然数有关的命题P(n)实际上是由无穷多个命题P(1)，P(2)，…，P(n)，……所组成，采用逐个论证的方法是不可能完成的。数学归纳法依据的是自然数的“归纳公理”：假设M是自然数集N的子集，如果满足①1∈M。②当k∈M时能推出k＋1∈M，那么M＝N。由归纳公理可以导出数学归纳法原理：设P(n)是与所有自然数n有关的命题 ，如果①P(1)是真命题。②当P(k)是真命题时能推出P(k＋1)也是真命题，那么对于任意自然数n，P(n)都是真命题。   数学归纳法的基本形式：对于与所有自然数有关的命题P(n)，如果能：①证明命题P(1)成立。②假设对于任意自然数k，P(k)成立，证明P(k＋1)也成立。则能断言命题P(n)对所有自然数n都成立。根据自然数集的“最小数原理”(即自然数集的每一个非空的子集必有最小数）可以推得数学归纳法的另一种形式(第二数学归纳法)：对于与所有自然数有关的命题P(n)，如果能：①证明命题P(1)成立。②假设对于任一自然数k，当1≤n≤k时 P(n)成立，证明P(k＋1)也成立。则能断言对所有自然数n，命题P(n)都成立。