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数学论证就是根据已知的公理、定理、定义、公式等数学命题来确定另一数学命题真实性的推理过程。下面是论证过程中应遵守的几项规则,否则犯逻辑错误。一、论题方面: (1)论题必须明确。若论题含糊不清,将犯“以讹传讹”的错误。例如,“两三角形相似时,求证它们的中线成比例”。这里的论题是含糊不清的:六条中线怎样成比例呢?即使“证池来”了,也是个假命题。只有在“中线”前面加上“对应边上的”这一条件,论题才算明确了。 (2)论题必须如一。若随时改变论题,将
Mathematical argumentation is based on known axioms, theorems, definitions, formulas and other mathematical propositions to determine the reasoning process of the authenticity of another mathematical proposition. The following are several rules that should be observed in the process of argumentation. Otherwise, they make logical mistakes. First, the topic: (1) The topic must be clear. If the topic is ambiguous, it will make a mistake of “using rumors.” For example, “If two triangles are similar, verify that their median line is proportional.” The topic here is ambiguous: how are the six midlines proportional? Even if the “certificate pool comes,” it is a false proposition. Only if the condition of “corresponding to the edge” is added before the “middle line”, the thesis will be clear. (2) The topics must be the same. If you change the topic at any time, you will