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A Comparative Analysis of Some Results from Qp and R

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  • Alin Cristian Ioan

    (University of Bucharest)

Abstract

The paper investigates whether a series of concepts and properties available in the real analysis remains valid for p-adic case. There are many similarities between R and Qp and also so many differences. First of all, R is an ordered field, which is not true for Qp. Secondly R is archimedean (that is the absolute valuation ? is archimedean) while Qp is not archimedean for any p prime. This means that R is a connected metric space while Qp is totally disconnected. This proves that there is no analogous notion of interval in Qp or a notion similar to the curve. These contrasts will cause the difference between the analysis p-adic and the real analysis.

Suggested Citation

  • Alin Cristian Ioan, 2014. "A Comparative Analysis of Some Results from Qp and R," Acta Universitatis Danubius. OEconomica, Danubius University of Galati, issue 10(5), pages 52-58, October.
    • Handle: RePEc:dug:actaec:y:2014:i:5:p:52-58
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    File URL: http://journals.univ-danubius.ro/index.php/oeconomica/article/view/2448/2247
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    Keywords

    p-adic; sequences; series; function;
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