A Simple Introduction to Nonstandard Analysis

  • Peter A. Loeb
Part of the Mathematics and Its Applications book series (MAIA, volume 510)


The notion of an infinitesimal number has been used in mathematical arguments since before the time of Archimedes, some 2200 years ago. We understand infinitesimals in terms of a scale set by ordinary numbers. For a positive number to be infinitesimal, it must be greater than 0 and yet smaller than any positive number you might write using a decimal expansion. No matter how many zeros you start with in that expansion, a positive infinitesimal number will be still smaller.


Number System Simple Sentence Nonstandard Analysis Transfer Principle Atomic Sentence 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Peter A. Loeb
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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