人们通过观察、度量、类比等方法猜想出许多数学结论,那么这些猜想是真还是假呢?若要说明它的正确性,只有一个途径———证明;若能找到一个反例(哪怕只有一个),即能说明它是错误的.这就是证明的必要性和反例的作用,请看下面的史料:一、期待证明的猜想哥德巴赫是德国一位中学教 People guess many mathematical conclusions through observation, metrics, analogies and other methods. So are these conjectures true or false? To illustrate its correctness, there is only one way—proving; if we can find a counterexample (even if there is only one) That is to say that it is wrong. This is the necessity of proof and the role of counterexamples. Please look at the following historical materials: First, the conjecture of proof of expectation Goldbach is a German secondary school teacher