English, Article, Journal or magazine article edition: A Total Order in [0,1] Defined through a 'Next' Operator Jaume Paradís; Pelegrí Viader; Lluís Bibiloni

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Bookmark: http://trove.nla.gov.au/version/153145
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • A Total Order in [0,1] Defined through a 'Next' Operator
Author
  • Jaume Paradís
  • Pelegrí Viader
  • Lluís Bibiloni
Physical Description
  • preprint
Notes
  • 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.
  • Total orders, pierce series, singular functions
  • RePEc:upf:upfgen:266
Language
  • English
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