哲学观点下的反演同构

Inversion Isomorphism under the Viewpoint of Philosophical

辩证矛盾的一分为二性,若换数学语言描述则称其为反演集合定义,即:论域中任一元素都有两面性,一面属正集合,另一面属反集合;正、反集合中元素一一对应,正集合与反集合互为反演集合。反演集合的结构包含反演测度、反演同构,可用于求事物的共同属性、判断事物相似性等;在有限群上同构是反演同构的特例,由此反演集合方法将经典数学方法中的同构和不同构拓展为同构、反演同构和不同构,从而能更加细致地对事物进行分类。

The dialectical contradictory one divided into two, in the mathematical linguistics is called the inversion set definition, namely ： any element has two sides. One side is being set, the other side are anti-set. The elements in the set and the anti-set are one- one mapping, the set and the anti-set are the inversion sets mutually. The inversion set structure contains the inversion measure and the inversion isomorphism which may be used in asking the common attribute of things, or judging the similarity and so on. Isomorphism on finite groups is a special case of the inversion isomorphism. From this, inversion set method extends isomorphism and not isomorphism in the classical mathematical method to isomorphism, inversion isomorphism and not isomorphism so as to enable more detailed classification of things.