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数学直觉是人们对数学对象的结构及其关系的某种直接领悟或者洞察,也就是说数学直觉是一种不包括演绎推理,不同于逻辑思维的一种直接感受,属于非形式逻辑思维的思想活动范畴.数学直觉也是合情推理的一种形式或者基础.一、数学直觉的特征和作用数学直觉具有明显的三个特征:(1)非逻辑性.正如波利亚所说:“直觉的洞察可能远远超前于形式逻辑的证明.”就是说,数学直觉往往不能用形式逻辑的推演先行解释.(2)自觉性.数学直觉的产生往往是在潜意识、下意识或无意识中自觉产生的.(3)简约性.数学直觉不同于严谨的逻辑
Mathematical intuition is a kind of direct comprehension or insight on the structure and relationship of mathematical objects. That is to say, mathematical intuition is a kind of direct feeling that does not include deductive reasoning, different from logical thinking, belongs to the thought of non-formal logical thinking The scope of activities.Mathematical intuition is also a form or foundation of co-rationality.First, the characteristics and the role of mathematical intuition Mathematical intuition has three distinct characteristics: (1) non-logical, as Polyglia said: Intuition "That is to say, mathematical intuition often can not be explained by the formal logic deduction. (2) Consciousness. The production of mathematical intuition is often consciously generated in subconscious, unconscious or unconscious (3) Contractivity Mathematical intuition is different from rigorous logic