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上海市新编数学课本中提出 :“要确定一个命题是假命题 ,只要举出一个满足命题条件 ,而不满足命题结论的例子就行了 .”这在数学中称为举反例 .教育理论认为 :概念或规则的正例传递了最有利于概括的信息 ,反例则传递了最有利于辨别的信息 .因此构造反例是我们辨析错误的重要工
In Shanghai’s new mathematics textbook, it is proposed that “To determine a proposition is a false proposition, simply quote an example that satisfies the propositional condition and does not satisfy the propositional conclusion.” This is known as a counterexample in mathematics. Educational theory states that: The positive examples of concepts or rules convey the information that is most conducive to the generalization, while the negative examples convey the information that is most conducive to discrimination. Therefore, constructing counterexamples is an important part of our analysis of errors.