Department of Economics and Business - Universitat Pompeu Fabra

Title:: A mathematical excursion: From the three-door problem to a Cantor-type perfect set
Authors:: Jaume Paradís, Pelegrí Viader and Lluís Bibiloni
Date:: June 1997
Abstract:: We start with a generalization of the well-known three-door problem: the n-door problem. The solution of this new problem leads us to a beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.
Keywords:: Pierce expansions, cantor-type sets
JEL codes:: C00
Area of Research:: Statistics, Econometrics and Quantitative Methods
Published in:: American Mathematical Monthly, 106, 3, (1999), pp. 241-251

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