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The reals as rational Cauchy filters

Weiss, Ittay (2016) The reals as rational Cauchy filters. New Zealand Journal of Mathematics, 46 . pp. 21-51. ISSN 1171-6096

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    Abstract

    We present a detailed and elementary construction of the real numbers from the rational numbers a la Bourbaki. The real numbers are defined to be the set of all minimal Cauchy filters in Q (where the Cauchy condition is defined in terms of the absolute value function on Q) and are proven directly, without employing any of the techniques of uniform spaces, to form a complete ordered field. The construction can be seen as a variant of Bachmann’s construction by means of nested rational intervals, allowing for a canonical choice of representatives

    Item Type: Journal Article
    Subjects: Q Science > QA Mathematics
    Divisions: Faculty of Science, Technology and Environment (FSTE)
    Depositing User: Ittay Weiss
    Date Deposited: 25 Jul 2016 14:16
    Last Modified: 25 Jul 2016 14:16
    URI: http://repository.usp.ac.fj/id/eprint/8818
    UNSPECIFIED

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