Continued radicals |
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| Authors: | Jamie Johnson Tom Richmond |
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| Institution: | (1) Department of Mathematics, Western Kentucky University, 1906 College Heights Blvd #11078, Bowling Green, KY 42101-1078, USA |
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| Abstract: | If a
1,a
2,…,a
n
are nonnegative real numbers and
, then f
1○f
2○⋅⋅⋅○f
n
(0) is a nested radical with terms a
1,…,a
n
. If it exists, the limit as n→∞ of such an expression is a continued radical. We consider the set of real numbers S(M) representable as a continued radical whose terms a
1,a
2,… 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.
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| Keywords: | Nested radical Continued radical Continued root |
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