Paper #239

Títol:

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

Autors:

Jaume Paradís, Pelegrí Viader i Lluís Bibiloni

Data:

Juny 1997

Resum:

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.

Paraules clau:

Pierce expansions, cantor-type sets

Codis JEL:

C00

Àrea de Recerca:

Estadística, Econometria i Mètodes Quantitatius

Publicat a:

American Mathematical Monthly, 106, 3, (1999), pp. 241-251

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