Continued Radicals

Authors Jamie Johnson, Tom Richmond

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Jamie Johnson
Tom Richmond

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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)


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.
  • Continued radical


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