counterexample

简明释义

英[ˈkaʊntərɪɡzɑːmpl]美[ˈkaʊntərɪɡzæmpl]

n. 反例

英英释义

单词用法

同义词

反义词

例句

1.Okay I gave you another test. That was one test of validity and another test I gave you was in the argument is valid if and only is it's counterexample set is inconsistent.

好，给你们另一个测试，这是有效性的测试，另一个是有效论点中，如果且仅如果这是不一致的反例。

2.If he could show us, he could convince us that harmony is not really invisible, then we would no longer have a counterexample to the claim that the invisible can't be destroyed.

如果他可以说服我们，和声并非无形，那我们就没有了，灵魂不可毁灭，这一论断的反例。

3.We particularly proved that 2 - sensitivity does not imply 3 - sensitivity by a counterexample.

特别地，通过反例证明了2-敏感不蕴涵3 -敏感。

4.Under his termination-deciding method, a nonterminating input can be further constructed as an counterexample for the given nonterminating loop, which makes the result more complete.

在其终止性可判定理论的基础上，对于给定非终止循环构造出其非终止输入作为反例，使该结果更加完整。

5.Is this a counterexample to the utilitarian idea of calculating?

这算是功利主义计算思路的反例吗？

6.Then, after the introduction and analysis of algorithm ASRAI we show a counterexample of this algorithm and present a revised algorithm CHEN1 to eliminate the disadvantage of algorithm ASRAI.

然后，通过对asrai算法的介绍与分析，举出asrai算法的反例，提出增量算法1以用于克服asrai算法存在的缺点。

7.There exists a counterexample showing that a compact topological space is not necessarily a sequentially compact space.

有反例表明一个紧致拓扑空间不一定是序列紧致的拓扑空间。

8.A valid argument cannot be disproven by a single counterexample.

一个有效的论点不能通过一个单一的反例来反驳。

9.In mathematics, a counterexample is used to disprove a statement or theorem.

在数学中，反例用于反驳一个陈述或定理。

10.The professor provided a counterexample to show that the hypothesis was incorrect.

教授提供了一个反例来表明假设是不正确的。

11.When discussing the theory, she mentioned a famous counterexample from set theory.

在讨论这个理论时，她提到了集合论中的一个著名反例。

12.He found a counterexample that illustrated the flaw in the proposed solution.

他找到了一个反例，说明了所提解决方案的缺陷。

作文

In the realm of logic and mathematics, the concept of a counterexample is crucial for testing the validity of statements or hypotheses. A counterexample is an instance that disproves a general claim or theory by providing a specific case where the claim does not hold true. Understanding this concept can greatly enhance our analytical skills and critical thinking abilities. For instance, consider the statement: "All swans are white." At first glance, this assertion seems reasonable based on observations in certain regions. However, the discovery of black swans in Australia serves as a counterexample, demonstrating that the original statement is false. This example illustrates how a single counterexample can refute a universally quantified claim. In academic discourse, the use of counterexamples is prevalent. When mathematicians propose a theorem, they often anticipate potential counterexamples that could challenge their assertions. This proactive approach not only strengthens their arguments but also fosters a deeper understanding of the concepts involved. For example, if someone claims, "If a number is even, then it is divisible by 4," a counterexample such as the number 2 can be presented to show that the claim does not hold true in all cases. Moreover, the importance of counterexamples extends beyond mathematics into everyday reasoning and decision-making. In debates, presenting a counterexample can effectively undermine an opponent's argument. For instance, if someone argues that all teenagers are irresponsible, one can cite examples of responsible young individuals as counterexamples. This method not only challenges the validity of the initial claim but also encourages a more nuanced discussion about the topic. Furthermore, in scientific research, counterexamples play a vital role in refining theories. When a scientist proposes a hypothesis, they must consider potential counterexamples that could invalidate their findings. This critical evaluation leads to more robust conclusions and advancements in knowledge. For instance, the theory that all bacteria are harmful was challenged by the discovery of beneficial bacteria, serving as a counterexample that reshaped our understanding of microbiology. In conclusion, the concept of a counterexample is indispensable in various fields, from mathematics to everyday reasoning and scientific inquiry. By recognizing and utilizing counterexamples, we can enhance our analytical abilities, strengthen our arguments, and foster a culture of critical thinking. The ability to identify a counterexample not only aids in disproving false claims but also promotes a deeper understanding of complex issues. As we navigate through life, embracing the idea of counterexamples can lead us to more informed decisions and a greater appreciation for the intricacies of knowledge.

在逻辑和数学领域，反例的概念对于检验陈述或假设的有效性至关重要。反例是一个实例，通过提供一个特定案例来证明一个普遍的主张或理论是错误的。在分析能力和批判性思维能力方面，理解这一概念可以极大地提升我们的技能。例如，考虑这个陈述：“所有天鹅都是白色的。”乍一看，这个说法似乎在某些地区是合理的。然而，在澳大利亚发现的黑天鹅就作为一个反例，证明了原始陈述是错误的。这个例子说明了单个反例如何推翻一个普遍量化的声明。在学术讨论中，使用反例是很常见的。当数学家提出一个定理时，他们通常会预见可能的反例，以挑战他们的论断。这种主动的方法不仅增强了他们的论点，还促进了对所涉及概念的更深入理解。例如，如果有人声称“如果一个数字是偶数，那么它可以被4整除”，那么数字2就可以作为一个反例，表明这个说法在所有情况下都不成立。此外，反例的重要性超越了数学，延伸到日常推理和决策中。在辩论中，提出一个反例可以有效地削弱对手的论点。例如，如果有人争辩说所有青少年都是不负责任的，那么可以引用负责任的年轻人作为反例。这种方法不仅挑战了初始声明的有效性，还鼓励对话题进行更细致的讨论。此外，在科学研究中，反例在完善理论方面发挥着至关重要的作用。当科学家提出一个假设时，他们必须考虑可能的反例，这些例子可能会使他们的发现失效。这种批判性评估导致更稳健的结论和知识的进步。例如，所有细菌都是有害的理论，因发现有益细菌而受到挑战，这个反例重新塑造了我们对微生物学的理解。总之，反例的概念在各个领域都是不可或缺的，从数学到日常推理，再到科学探究。通过识别和利用反例，我们可以增强我们的分析能力，强化我们的论点，并促进批判性思维的文化。识别反例的能力不仅有助于驳斥虚假的主张，还促进了对复杂问题的更深刻理解。在我们生活的旅程中，接受反例的理念可以引导我们做出更明智的决策，并更深刻地欣赏知识的复杂性。