众所周知,数学中要判断一个命题是正确的,必须经过严密地论证,而要说明一个命题是错误的,只需举出一个与结论相矛盾的例子即可.如要否定“两个无理数的和是无理数”,只要举出反例 (2+2~(1/2))+(3-2~(1/2))=5就可以了.反例因其具有直观、明显、形象、生动等特点,决定了它在数学教学中无可比拟 As we all know, in mathematics, to judge a proposition is correct, it must be rigorously demonstrated, and to illustrate that a proposition is wrong, just give an example that is inconsistent with the conclusion. If you want to negate the “sum of two irrational numbers, It is an irrational number”, as long as the counterexample (2+2~(1/2))+(3-2~(1/2))=5 is sufficient. The counterexample is characterized by being intuitive, obvious, vivid and vivid. , it is unparalleled in mathematics teaching