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特殊与一般是反映事物间某种相对关系的重要哲学范畴对,也是反应“活数学的深刻本质”的三对范畴(一般与特殊、演绎与构造、逻辑与想象)之一,在数学的发展过程中,既有一条从特殊到一般的发展脉络,也有一条与之相对的从一般到特殊的发展脉络,二者相互作用,合成了数学发展的弯弯曲曲之路。一、特殊化思维方法特殊化是把所研究的数学问题从原来的范围缩小到一个较小范围或个别情形进行考察研究的思维方法。将问题向特殊的形式转化,得到一个新的数学问题,
Particularity and generality are important pairs of philosophical categories that reflect some relative relationship between things and also one of three categories (generality and specialness, deduction and construction, logic and imagination) that reflect the “deep nature of living mathematics.” In mathematics The development process, both from a special to the general context of development, there is also a relative to the general from a special context of development, the interaction between the two, the synthesis of mathematical development of the winding road. First, the specialization of the thinking method Specialization is to study the mathematical problems reduced from the original scope to a smaller area or individual case study approach to thinking. Transform the problem to a special form, get a new mathematical problem,