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存在性命题在其结论中大多有“有一个”、“存在一个”等这样的量词,一般都可表示成这样的形式:已知A1,求证存在事物A2,使A2具有性质A3.求解存在性问题的方法通常有两类,一类是反证法;另一类是构造性,即构造出具有性质A3的事物A2以完成证明.比较而言,构造性证明一般都有较高的技巧要求,强化这方面的训练对优化数学思维、提高学科素养、提高解题能力都颇有益处.例1设a,b,c,d都是正数,求证:有一个
Existence propositions in the conclusion are mostly quantifiers such as “there is a ”, “there is a ” and so on, which can generally be expressed in the form of knowing A1, verifying that there exists something A2 and making A2 a property A3 There are generally two ways to solve existential problems, one is anti-syndrome, the other is constructive, that is, construct A2 with property A3 to complete the proof, while the constructive evidence generally has higher Skill requirements, strengthen training in this area to optimize the mathematical thinking, improve academic quality, improve the ability to solve problems are quite good.Example 1 Let a, b, c, d are positive, verify: there is a