1, induction:
Induction draws a general conclusion through the analysis of special cases. When studying general problems, we should first study several simple, individual and special situations, from which we can sum up general laws and properties. This kind of reasoning from part to whole, from special to general, is called induction.
2. Deduction:
Deduction, contrary to induction, is to draw individual or special conclusions from general conclusions or general premises. When studying individual problems, based on general logical assumptions, specific conclusions are drawn. This reasoning from the general to the specific is called deduction.
3. Analogy:
Analogy is a kind of reasoning from special to special, which contains assumptions and guesses. Like induction, analogy is a common rational reasoning. On the basis of existing knowledge, analogy draws new guesses from existing knowledge through some identical or similar properties between two (or more) objects, and infers that they are identical or similar in other properties.
4. Classification:
Classification is based on comparison. According to the similarities and differences of the essential attributes of mathematical research objects, mathematical objects are divided into different categories. The classification of mathematical objects must be scientific and unified, and each classification can only have one standard, and several different standards cannot be used interchangeably, so that the classification is not repeated or omitted.