本文从自然数及其记数法的基本概念出发，辨析了与二进位制相关的几个容易混淆的概念，指出序数概念的引入在近代数学发展中有重要意义，作为邵雍数学学派的数学基础，先天易是数学史上第一个专门定义的序数体系，该序数体系在数学史上率先采用了二进位制记数法。先天易作为二进制序数体系这一事实在明清时期引起不同的反响，反对者认为它使易道沦落，大数学家汪莱则从P进制的角度论证它的优越性。本文最后还对近年来反对先天易与二进制有关的两种典型观点进行了剖析，指出其谬误所在。
关键词：先天易； 二进位制； 序数； 邵雍；汪莱
A research on the mathematics foundation in the primordial Yi
——on the primordial hexagrams\' order and binary system
KE Zi-neng
(Department of Science-technology History & Archaeology, Science-technology University of China, Hefei 230026, China)Abstract: Departing from basic concepts of cardinal numbers and their numbering orders, the paper differentiated and analyzed some concepts easy to be confused related to binary system, pointing out that the introduced concepts of ordinals played an important role in the development of modern mathematics. As the foundation of SHAO Yong\'s mathematics, the primordial Yi, in the history of mathematics, exhibits the first specially defined ordinal system, in which the binary numbering method was used at the first time. Being a binary ordinal system, the primordial Yi aroused different repercussions: opposers censured it debased Yi; While, departing from the angle of the P carrying system, WANG Lai, a great mathematician, proved its superiority. In addition, the paper also analyzed two typical viewpoints against the primordial Yi and binary system, to expose their fallacy.
Key words: the primordial Yi; binary system; ordinals; SHAO
Yong; WANG Lai
