数学的基础:存在——觉数能力——不确切数——数量体系

The Foundation of Mathematics:Being——the Sense of Mathematics——Indefinite Number——Number System

以"天人知识"认知理论体系(N+H=K)和相关的"知识-非知识"、"科学-非科学"划界标准为基础理论,以人类科学中的相关史料及新成果为基本素材,探讨数学基础理论中"存在"、"觉数能力"、"觉数行为"、"实无穷-潜无穷"、"确切数"与"不确切数"这几个重要概念及之间的必然联系,在一个新的数学哲学理论体系中进一步分析、研究、认识与"无穷"概念相关的"数"及其"数量体系"的本质,认识与"不确切数"相关且有别于传统"形式分类法"的几种新数量体系.

Based on the cognitive theory of the theory that knowledge is an integration of man and nature（N＋H=K） and its related standards of ＂knowledge-non-knowledge demarcation＂ and ＂science-non-science demarcation＂,with the historical material and the new achievements in our science as basic source material,the important connotations of ＂being＂,＂the sense of mathematics＂,＂the behavior of mathematics＂,＂actual infinity-potential infinity＂,＂definite number＂ and ＂indefinite number＂ and their natural relationship in the foundation of mathematics are discussed.The natures of ＂number＂ and the ＂number system＂ closely related to the ＂infinite＂ concept are further analyzed and studied in a new theoretical system of the philosophy of mathematics,and the new number systems different from the traditional ＂form classification＂ and related to the ＂indefinite number＂ are developed.