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9 非标准分析的现状简介前面已提到,在微积分出现大约300年之后,美国数学家鲁宾孙又复活了牛顿和莱布尼兹那种无穷小的数,重新把微积分建立在无穷小的数的基础上.鲁宾孙说:“1960年秋,我想到了现代数理逻辑的概念和方法能够为运用无穷小和无穷大的数来叙述微积分学提供一个合适的框架.我先是在普林斯顿大学的一个讨论班(1960年11月)的报告中说明了我的想法.随后又在符号逻辑学会年会(1961年1月)的一次发言中,以及刊登在阿姆斯特丹皇家科学院院报的论文(Non-standard Analysis)中,相继发表了我的想法.我把所得到的这个课题叫做非标准分析,因为它包含有所谓算术的非标准模型,并且部分地是受到了后者的启发.”1966年出版了罗宾孙的书《非标准分析》(有中译本),在该书第二版(1974年)前言中,当代大数学家哥德尔(K.G(?)del,
9 Non-standard analysis of the status quo Introduction Mentioned earlier, about 300 years after the calculus, the American mathematician Rubin Sun resurrected the infinite number of Newton and Leibniz, re-calculus built on infinitesimal On the basis of the number, Rubin Sun said: “In the fall of 1960, I came to mind that the concepts and methods of modern mathematical logic can provide a suitable framework for describing calculus using infinitesimals and infinitesimal numbers.I first at Princeton University My thoughts were illustrated in a report in a workshop (November 1960), later in a speech at the annual meeting of the Symbolic Logic Society (January 1961), and in a paper published in the Proceedings of the Royal Academy of Sciences in Amsterdam (Non- standard Analysis, I published my thoughts one by one, and I called this topic a nonstandard analysis because it contains nonstandard models of so-called arithmetic and is partly inspired by the latter. ”1966 Published Robin Sun’s book Nonstandard Analysis (with Chinese translation), in the preface to the second edition of the book (1974), the current great mathematician Gödel (KG (?) Del,