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反例是指符合命题条件而不符合该命题结论的例子。简言之,反例就是能够说明一某命题不成立的例子(即假命题)。数学中的反例的主要作用是证伪(即说明某一个命题不正确),当直接证明某个命题是假命题或说明某些猜想错误比较困难时,常常会趋向于寻找一个反例,以说明这个命题或猜想是错误的,在数学教学中,恰当地运用与建构反例进行数学教学,有助于学生深刻理解与掌握,有助于培养学生思维的灵活性与深刻性。本文从反
Counterexamples refer to examples that conform to the propositional conditions and do not conform to the conclusions of the proposition. In short, counterexamples are examples (ie, false propositions) that illustrate the untrustworthiness of a proposition. The main role of counter-examples in mathematics is to falsify (that is, to say that a certain proposition is not correct). When directly demonstrating that a proposition is a fake proposition or explaining some guessing error is difficult, it tends to look for a counterexample to illustrate this Proposition or conjecture is wrong. In mathematics teaching, the proper use and construction of counterexamples in mathematics teaching will help students to understand and master deeply, and help to cultivate the flexibility and profoundness of students’ thinking. This article from the anti