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Turkish Journal of Mathematics

HÜLYA DURU

DOI

-

Abstract

The concept of the ``relation of comparability'' was introduced by Maillet in [7], who showed that if \alpha,\beta are comparable Liouville numbers then each of the numbers \alpha +\beta, \alpha -\beta, \alpha \beta and \alpha /\beta is either a rational or Lioville number. Moreover those which are Liouville numbers are comparable aamong theem and to \alpha and \beta. Maillet's proof uses in an essential way the transitivity of the comparability relation. Unfortunately, as the comparability relation is not transitive, his proof is defective. In this paper, without using the comparability relation, we obtain some uncountable subfields of p-adic numbers field, Q_p. In [1] using a different notion of comparability, Alnıaçık was able to define some uncountable subfields of C. In this paper, without using comparability relation, we define irregular semi-strong p-adic U_m numbers and obtain some uncountable subfields of p-adic numbers field Q_p

First Page

75

Last Page

85

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