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8 标准分析的现状简介17世纪后半期,牛顿和莱布尼兹首先使用无穷小建立了微积分的基本概念,但是其推理过程却存在着显著的矛盾,在后来长达200年的时间里,经过达兰贝尔、哥西以及外尔斯特拉斯等人的努力,终于建立了严格的极限理论,把微积分的基本概念全部建立在极限概念之上,使得上述矛盾第一次被成功地消除。与此同时,也把牛顿和莱布尼兹的那种无穷小彻底地赶出了微积分阵地,并且使用无穷小变量,即其极限为零的变量代替了无穷小的数。但是,大约又过了100年,即微积分出现大约300年之后,美国数学家鲁宾孙(Abraham Robinson,1918
8 Standard Analysis of the status quo Brief introduction The late 17th century, Newton and Leibniz first infinitesimal calculus established the basic concept, but its reasoning process there are significant contradictions, then up to 200 years later, after The efforts of Dalai Laer, Gossi and Foreign Strathlt finally established a strict limit theory, based on the concept of the limits of all the basic concepts of calculus, making the above contradictions successfully eliminated for the first time . At the same time, Newton and Leibniz were also completely expelled from the calculus of infinitesimals, and infinitesimal variables were replaced with infinitesimal variables, ie variables whose limits were zero. However, about another 100 years later, after about 300 years of calculus, the American mathematician Abraham Robinson (1918