DagSemProc.04351.10.pdf
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Continued Radicals
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Dagstuhl Seminar Proceedings, Volume 4351
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2005-04-22
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Jamie Johnson and Tom Richmond. Continued Radicals. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.04351.10
https://doi.org/10.4230/DagSemProc.04351.10
Abstract
A nested radical with terms $a_1, a_2, \ldots , a_N$ is an expression of form $\sqrt{a_N + \cdots + \sqrt{a_2 + \sqrt{a_1}}}$. The limit
as $N$ approaches infinity of such an expression, if it exists,
is called a continued radical. We consider the set of real
numbers $S(M)$ representable as a continued radical whose terms $a_1, a_2, \ldots$ are all from a finite set $M$ of nonnegative real numbers. We give conditions on the set $M$ for $S(M)$ to be (a) an interval, and (b) homeomorphic to the Cantor set.
Keywords
- Continued radical
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