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A mathematical excursion: From the three-door problem to a Cantor-type perfect set
Paradís, Jaume; Viader, Pelegrí; Bibiloni, Lluís
Universitat Pompeu Fabra. Departament d'Economia i Empresa
We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa 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.
Statistics, Econometrics and Quantitative Methods
pierce expansions
cantor-type sets
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