Paper #266

Title:

A total order in [0,1] defined through a 'next' operator

Authors:

Jaume Paradís, Pelegrí Viader and Lluís Bibiloni

Date:

January 1998

Abstract:

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}n are all dense in R1 and are constituted by elements of the same arithmetical character: if a is an algebraic irrational of degree k all the elements in a's orbit are algebraic of degree k; if a is transcendental, all are transcendental. Moreover, the asymptotic distribution function of the sequence formed by the elements in any of the half-orbits is a continuous, strictly increasing, singular function very similar to the well-known Minkowski's ?(×) function.

Keywords:

Total orders, pierce series, singular functions

JEL codes:

C00

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

ORDER, 16, 3, (1999), pp. 17-30

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