Type of Document Master's Thesis Author Lengyel, Eric URN etd-10012008-063105 Title Hyperreal structures arising from an infinite base logarithm Degree Master of Science Department Mathematics Advisory Committee

Advisor Name Title No Advisors Found Keywords

- infinitesimals
- hyperreal numbers
- nonstandard analysis
- limits
- infinite series
Date of Defense 1996-04-11 Availability restricted AbstractThis paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of "nonstandard analysis". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the fundamental results of nonstandard analysis which are used throughout the paper. The new theory which is built upon this foundation organizes the set hyperrea.l numbers through structures which on an infinite base logarithm. Several new relations are introduced whose properties enable the simplification of calculations involving infinite and infinitesimal The paper explores two areas of application of these results to standard problems in elementary calculus. The first is to the evaluation of limits which assume indeterminate forms. The second is to the determination of convergence of infinite series. Both applications provide methods which greatly reduce the amount of con1putation necessary in many situations.

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