论文部分内容阅读
存在型问题,一般有肯定型、否定型和讨论型三种,即在数学命题中,常以适合某种性质的结论“存在”、“不存在”、“是否存在”等形式出现．“存在”就是有适合某种条件或符合某种性质的对象,对于这类问题无论用什么方法只要找出一个,就说明存在．“不存在”就是无论用什么方法都找不出一个适合某种已知条件或性质的对象,这类问题一般需要推理论证．“是否存在”结论有两种:可能,或存在,需要找出来;若不存在,则需说明理由．在处理过程中,对于一些存在型问题,我们常常先假设结论中相对独立的某一方面成立,进行演绎推理,若出现矛盾,即可否定先前的假设,而得出相应的结论;若推出合理的结果,且推理过程可逆,说明假设正确．
There are three types of problems: existence-type, negative-type, and discussion-type. In mathematics propositions, the form of “existence”, “non-existence”, “existence”, etc. often appears in a form suitable for a certain nature. “Existence” means that there is an object that fits a certain condition or meets a certain nature. For any problem of this kind, just find one and show that it exists. “No existence” means that no matter what method is used to find an object that is suitable for a certain known condition or nature, such problems generally require theoretical verification. There are two kinds of “whether or not there are” conclusions: they may be or exist, and they need to be found out; if they do not exist, they must explain the reasons. In the process of handling, for some existing problems, we often assume that a relatively independent aspect of the conclusion is established and deductive inference. If there is a contradiction, we can negate the previous assumption and arrive at a corresponding conclusion; if reasonable The result of the inference process is reversible, indicating that the hypothesis is correct.