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The paper studied how to structure a kind of counterexample function in the analysis and widespread application emphatically, further pointed out the misunderstandings easily appeared in the concept and theorem of continuity, derivable, integrable, and other analytic properties of the function and gave the corresponding counter-example finally.

研究了一类函数在分析学相关反例构造中的应用,进一步指出有关函数的连续、可导、可积等分析性质的概念与定理中容易出现的误区,并给出相应的反例,希望能引起高校师生对该类函数的重视,进一步提高教学效果。

The text introduces the probability of random events and issues of counter-examples; discrete random variables related to the distribution and continuous random variable distribution of counter-examples; independence and related issues in the Phase capacitive on the counter-examples; number of characteristics of the random variable The counter-examples of; parameters estimates and assumptions in the anti-testing case of problems.

该文主要介绍了随机事件及其概率问题中的反例;有关离散型随机变量分布和连续型随机变量分布中的反例问题;独立性与相关性相容性问题中的反例介绍;有关随机变量数字特征的反例探讨;有关参数估计与假设检验中的反例问题。

This is the crux of Gettier counter examples, each example has a problem involving the justification.

这就是"葛梯尔反例"的关键所在,每个反例都涉及一个"证明"的问题。

The second part points out the weakness in the planar graph of Heawood's counter example and also its types by GR graph. It also offers a new type of counter example so as to replace the former one.

第二部分通过GR图对希伍德反例进行了深入的探讨,指出该类型的平面图自身有破绽并给出新的反例类型以取代原反例

It is a hot research topic to eliminate irrelevant variables from counterexample, to make it easier to be understood.

使用反例压缩算法,从反例中剔除冗余信息,从而使反例易于理解,是目前的研究热点。

At last, a counterexample generation algorithm is presented to generata debug information for finding and modifing design errors.

如果验证失败,则通过反例生成算法,给出反例信息,供设计人员查找和修改错误时参考。

But traditional model checkers give users a single counterexample, chosen from the set of faulty behaviors. So it's also necessary to study how to give the user access to the entire set.

但传统的模型检查器只能为用户从错误行为集合中提供一个反例,这就影响了模型检查的效率,如何让用户可以得到全部的反例,也是需要研究的问题。

Three counter-examples of topological space are proposed in this study: There are two metric spaces, X and Y, in which and are isometric, whileand are not isometric; Non-metric tight regular space is a counter-example of the separation of topological space; No non-zero continuous linear functionals of the linear topological space is a counter-example of linear topological space.

这里给出三个反例,存在两个度量空间X与Y,使X^2与Y^2等距而X与Y并不等距是拓扑空间中的反例;存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例;不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例

Even thought the students tell the illustration and the proposition correctly, only few of them know that merely one counter-example is needed to contradict the proposition. Most students are rather inclined to regard the counter-example as restrictions and exceptions just like Lakatos says when the number of counter-example is less and example more than contradict proposition of examples. As a result, they are less able to deny negative proposition.

结果发现即使拥有正确判断图例与命题间关系的学童,在面临同时有正反例图例时,只有极少数学生知道只要一个反例就可驳斥命题,大部分学生在反例较少而正例多时,会倾向如Lakatos所描述把反例视为题目的限制或是特例,而不与有较多正例支持的命题陈述来冲突,故较无法正确拒绝错误命题。

At first, in this paper, the concept and type were introduced; afterwards, how to apply counter-examples in the higher mathematics was expatiated particularly in such aspects: concept、theorem、rule、formula and distinguishing true and false of the proposition; Finally, the construction of counter-examples was explored using special example、character、the method of approach as well as intuitional geometrical graphics.

本文首先简要介绍了反例的概念和类型;然后从概念、定理、法则、公式以及判别命题真假等几个方面,详细阐述了在高等数学中如何应用反例;最后,从利用特例、性质,采用逼近的方法以及直观的几何图形几个方面探讨反例的构造。

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