Continued Radicals
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 r...
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TopSCHOLAR®
2005
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ndltd-WKU-oai-digitalcommons.wku.edu-theses-12432013-01-08T18:57:33Z Continued Radicals Johnson, Jamie 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. 2005-01-01 text application/pdf http://digitalcommons.wku.edu/theses/240 http://digitalcommons.wku.edu/cgi/viewcontent.cgi?article=1243&context=theses Masters Theses & Specialist Projects TopSCHOLAR® Radical Numbers Mathematics Geometry and Topology Mathematics |
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Others
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NDLTD |
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Radical Numbers Mathematics Geometry and Topology Mathematics |
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Radical Numbers Mathematics Geometry and Topology Mathematics Johnson, Jamie Continued Radicals |
| description |
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. |
| author |
Johnson, Jamie |
| author_facet |
Johnson, Jamie |
| author_sort |
Johnson, Jamie |
| title |
Continued Radicals |
| title_short |
Continued Radicals |
| title_full |
Continued Radicals |
| title_fullStr |
Continued Radicals |
| title_full_unstemmed |
Continued Radicals |
| title_sort |
continued radicals |
| publisher |
TopSCHOLAR® |
| publishDate |
2005 |
| url |
http://digitalcommons.wku.edu/theses/240 http://digitalcommons.wku.edu/cgi/viewcontent.cgi?article=1243&context=theses |
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AT johnsonjamie continuedradicals |
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1716574152345780224 |