A Simple Introduction to Nonstandard Analysis
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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.
KeywordsNumber System Simple Sentence Nonstandard Analysis Transfer Principle Atomic Sentence
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- 3.H. J. Keisler, Elementary Calculus, An Infinitesimal Approach, first edition 1976, second edition 1986, Prindle, Weber & Smith, Boston.Google Scholar