摘要
无极、太极、阴阳与数学相关概念具有对应关系:无极对应空集、数字0、初始原点;太极对应全集、数字1、单位圆;阴阳对应全集的二元对立划分,数字0、1组合或0、1字符串,单位圆的二元切分(上、下半圆与左、右半圆).给出了阴阳的集合描述性定义、阴阳的集合划分定义、阴阳关系(广义)基本方程组.讨论了两个集合等式A∩B=∅,AUB=I与对立统一的关系,以及阴阳集合与互补集合、阴性阳性事件与对立事件之间的关系.由阴阳的集合划分定义给出了阴阳集合的基本性质,进而导出了阴阳变化的基本规律.
Abstract
This paper investigated the corresponding relationships between wuji(无极),taiji(太极),yin-yang(阴阳)and certain mathematical concepts,i.e.wuji directly corresponds to the empty set,the number 0 and the intial origin;taiji corresponds to the universe set,the number 1 and the unit circle;yin-yang directly corresponds to the binary opposition division of universe set,the combination of numbers or characters 0 and 1,and the binary divi-sion of unit circle(into upper and lower semicircles,or left and right semicircles).In addition,the definitions of set descrication,set partitioning,and the set of basic equations(in a generalised sense)for yin and yang were given.The relationships between two set equations A ∩ B=∅,A U B=I and unity of opposites were discussed,and the relationships between yin-yang sets and mutual complementary sets,oppositional events of yin and yang were explored.The basic properties of yin-yang sets are illustrated by the definition of yin-yang set partitioning,so as to reveal the basic laws of yin-yang transformation.
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