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众所周知,要判断一个命题的正确与否必须经过严密的推证,而要否定一个命题,只要举出一个与结论相矛盾的例子即可,这种与命题相矛盾的例子称为反例。举反例和证明都是重要的数学思维方式,它们是一个问题的两个侧面。美国数学家B.R.盖尔鲍姆和J.M.H.奥姆斯特德指出:“冒着过于简单化的风险,可以说数学由两大类——证明与反例组成,而数学的发现也是朝着两个主要的目标——提出证明与构造反例。”所以可以认为
It is a well-known fact that to judge whether a proposition is correct or not must be strictly inferred and to deny a proposition simply by contradicting the conclusion with a conclusion. Such contradictory example is called counterexample. Both counter-examples and proofs are important mathematical ways of thinking, and they are two sides of a problem. The American mathematician BR Gaelbaum and JMH Olmsted argue that “there is a risk of simplistic simplification. It can be said that mathematics consists of two major categories - proof and counterexample, and the discovery of mathematics is also toward two The main goal - to prove and construct counterexample. ”So can think