A Comparative Analysis of Some Results from Qp and R

• Main Author: Alin Cristian Ioan
• Format: Article
• Language: English
• Published: Danubius University 2014-10-01
• Series: Acta Universitatis Danubius: Oeconomica
• Subjects: p-adic; sequences; series; function
• Online Access: http://journals.univ-danubius.ro/index.php/oeconomica/article/view/2448/2247

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.