If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.
| Identifer | oai:union.ndltd.org:WKU/oai:digitalcommons.wku.edu:theses-1243 |
| Date | 01 January 2005 |
| Creators | Johnson, Jamie |
| Publisher | TopSCHOLAR® |
| Source Sets | Western Kentucky University Theses |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses & Specialist Projects |
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