A mathematical excursion: From the three-door problem to a Cantor-type perfect set

Jaume Paradís (), Pelegrí Viader () and Lluís Bibiloni
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Pelegrí Viader: https://www.upf.edu/web/econ/faculty/-/asset_publisher/6aWmmXf28uXT/persona/id/3418630

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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 (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 1997-06
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:239

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