其中一条关于试图回答休谟理论的便是，归纳法实际上可以经由纯粹的推理证明，而不是演示，诉之于概率的除外。
One way of trying to answer Hume is to show that actually induction can be justified by pure reason but by appeal to probability rather than demonstration.
即便我们的归纳证明不能依赖纯粹的推理，对于归纳法实用主义的论证尝试也会得以体现。
And the Pragmatic Justification of induction attempt have been made to show that even if we cannot justify relying on induction by pure reason.
不难利用归纳法证明上面两个性质。
It is not hard to prove the above two properties by induction.
将压缩域关键视频对象选择算法形式化为压缩域关键视频对象选择模型，证明该模型满足归纳法准则；
Also, the course of IKVOS in the compressed domain is formalized and the model of IKVOS is proved to satisfy the criterion of coinduction.
数学归纳法可以用来证明与正整数有关的恒等式、不等式、整除性问题和几何问题等。
Mathematical induction can be used to prove the positive integers and Identities, inequality, and the divisibility of geometric problems.
图的可收缩边与可去边是研究连通图的构造和使用归纳法证明连通图的一些性质的有力工具。
Contractible edges and removable edges in connected graphs are a powerful tool to study the structures of connected graphs and to prove some properties of connected graphs by induction.
在具体的证明过程中，主要使用的是关于公式结构的归纳法。
In the proving process, we mainly use the induction on the formula structure.
讨论了一类根式的无理性，并用数学归纳法给出了证明。
This paper discusses a type of method of radical irrational using mathematical induction.
本文列举了归纳法在高中几种类型证明中的应用。
This article cited the induction of several high schools in the application of that type.
类比关于数式的二项式定理，导出关于矩阵的二项式定理，并用数学归纳法予以证明，最后举例说明关于矩阵的二项式定理的应用。
Compared to digital binomial function, matrix binomial function is derived and proved with induction method and the application of it is illustrated with examples.
利用数学归纳法证明了一个关于正值函数的不等式，并举例说明了其应用。
This paper proves an inequality based on a positive function with mathematical induction and demonstrates its application with examples.
对数学归纳法逻辑基础即原理的准确理解，是教师进行数学归纳法教学的前提，也是学生能否掌握这种证明方法的关键。
On the logical basis that the principle of mathematical induction accurate understanding of the teachers teaching mathematical induction premise is that students can grasp the key method.
应用数学归纳法验证了“倒三角形”一些性质的存在性，并给出这些性质的证明。
Mathematic induction is used to validate the existence of nature of the Up-side Down Triangle and its testification is given in the paper.
利用数学归纳法证明算法对任意多个离散点三角形网格剖分的正确性，并通过试验验证了算法的可行性。
The mathematical induction is used to prove the correctness of the algorithm towards the triangle mesh of random multi-points, and the experiment proves its feasibility.
数学归纳法是一种证明与正整数有关的命题的极为有效的科学方法。
Mathematical induction is a positive integer proved extremely relevant to the topic of effective scientific methods.
运用范数不等式，使用数学归纳法，证明了几个范数等式。
Several norm equalities are proved by norm inequality and mathematics induction.
论文用两种方法给出了广义超立方体网络宽直径的具体证明，而两种方法的主要区别在于分别采用数学归纳法和直接构造法证明了不等式(1)。
In this paper, the wide-diameter of generalized hypercube is proved in two ways whose difference is to use mathematical induction and constructing method to prove the inequation (1).
数学归纳法是数学中常常用到的一种证明方法，最常见而最为人们所熟知的归纳途径是简单的有向路。
The mathematical induction is a method of proof often applied in mathematics. The most common and the most famous inductive way is the simple directed path.
作出归纳法假设，进行简单的归纳法证明。
Synthesize induction hypotheses and simple induction proofs.
同时我指出了希伍德对顶点数套用数学归纳法的格式来证明“五色定理”的方法是错误的，从而否定了希伍德证明的“五色定理”。
I is pointed out that Heawood applied the mathematical induction for the vertex number to prove 'The Five Color theorem' is incorrect.
本文按照这种算法总结出完成四柱汉诺塔游戏之最少步数的公式，并用数学归纳法证明了它。
According to that algorithm, this article puts forward a formula to calculate the number of movements necessary for the 4-peg Hanoi Tower problem, and proves it using mathematical induction.
本文按照这种算法总结出完成四柱汉诺塔游戏之最少步数的公式，并用数学归纳法证明了它。
According to that algorithm, this article puts forward a formula to calculate the number of movements necessary for the 4-peg Hanoi Tower problem, and proves it using mathematical induction.
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