Title page for ETD etd-10012008-063105
|Type of Document
||Hyperreal structures arising from an infinite base logarithm
||Master of Science
|No Advisors Found
- hyperreal numbers
- nonstandard analysis
- infinite series
|Date of Defense
This 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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