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| 反例在数学中的作用 中文摘要： 数学学科具有典型的严谨、缜密特点，它已经构建了逻辑推理与思维模式，在数学发展过程中，反例的重要性十分突出，与证明具有基本一致的地位。特别是在揭露事物虚假性过程中，有着自身独特效果，作用十分突出。 反例，就是举出一个案例，证明当前的命题不成立，这个案例不仅满足命题条件，但是其最终的结论与命题结论存在矛盾。在数学命题证明过程中，要证明在给定的条件下，相关结论都能够成立。但是若是要否定一个命题，只需要在命题条件满足基础上证明和结论不统一，只需要举出相应反例便可。 关键词：反例 来源 构造 辨证 作用 Abstract: Mathematics is a rigorous science, it has its own unique way of thinking and logic reasoning system, in the process of mathematical evolution, the importance of counterexamples is consistent with the proof, especially in the aspect of false transaction, has its special charm, plays a very important role. So-called counterexample is usually used to indicate a proposition is not established, which can meet the requirements of proposition but inconsistent with the conclusion that the proposition of cases. Founded in mathematics to prove that a proposition, in accord with the topic will be strictly argument set all kinds of possible conclusions are set up, and to overthrow a proposition, but as long as you pointed out that in accord with the topic of a particular situation to conclusions, or just give a counter example. Keyword:counter-examples source structure dialectical role |
