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Tension between Intuitive Infinitesimals and Formal Mathematical Analysis

2011/10/26 by Mikhail G. Katz, Katz, Mikhail G., David Tall +1
Mathematics · #01A85 #03A05 #26E35 #97A20 #97C30 #FOS: Mathematics #History and Overview (math.HO) #Logic (math.LO) #math.HO #math.LO #msc:01A85 #msc:03A05 #msc:26E35 #msc:97A20 #msc:97C30

paper · pdf · doi:10.48550/arxiv.1110.5747

19 pages, 5 figures, Chapter in: Bharath Sriraman, Editor. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast Monographs in Mathematics Education 12, Information Age Publishing, Inc., Charlotte, NC, 2011. See http://www.infoagepub.com/products/Crossroads-in-the-History-of-Mathematics

arxiv created 2011/10/26 · arxiv updated 2011/10/27

Abstract

We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of mathematical thinking and imaginative visual interpretations of axiomatic proof.

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