解决数学中一个未解之谜的新途径(英文)

A New Way Out of Pending Problem in Mathematics

传统有穷、无穷理论体系决定了与之相关的数谱为０零０—无穷小△有穷数∞无穷大，现有几代数学分析理论都是在传统无穷观中，在这样的数谱内思维的，这深层结构中的等价性决定了第二次数学危机无法得到解决。作者讨论了数学分析中未解决的新、旧悖论及传统无穷观中的缺陷，引进三种新数，即过渡小，过渡大和彦，构造一个新数谱：０零０—无穷小０＋过渡小△有穷数∞＋过渡大∞—无穷大∞彦。新数谱的产生是对“数”概念认识的一大飞跃，标志着新无穷观的产生及新一代数学分析理论的诞生。

The traditional finite infinite concept system produces the following number spectrum:0zero 0—infinitesimal △finite number ∞infinity.All the old and new theories of mathematical analysis are working within this number spectrum.It is such an equivalence in the theories’ deep structure that decides the second mathematical crisis can not be solved at all.The writer studies the unsolved old and new paradoxes in mathematical analysis as well as the defects in the traditional finite infinite concept system,introduces three new forms of number and creates following new number spectrum:0zero 0—infinitesimal 0+intersmall △finite number ∞+intergreat ∞—infinity∞yan.The discovery of three new number forms and the construotion of the new number spectrum is a great leap forward for understanding “number”.Our work proclaims the birth of the new finite infinite concept system and brings about the birth of the new generation of mathematical analysis.