Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14592
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Main Title: Prinzipien einer Standard Analysis
Author(s): Pfender, Michael
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15819
http://dx.doi.org/10.14279/depositonce-14592
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: We introduce formally small entities such as ε,dx,dy etc. as non-zero null sequences of rational numbers. All rational sequences form an extended do- main R of real numbers, extended by small, big and non-convergent numbers. Differenzials are introduced as small differences, integrals as infinite sums over small parts. This is to give a formal background to notions and some basic theorems of real analysis before the 19th century. In a second part an attempt is made to a Quaternion Analysis based on the above principles of a formalised standard real analysis. We continue with an Analysis of a 12-dimensional Vektoralgebra obtained from the algebra of quaternion quaternions by quotient formation and shrinking 2 dimensions to smallness. It is hoped that this analysis could be usefull for geometry and for mathematical physics.
Subject(s): real functions
real numbers
quaternion analysis
Issue Date: 3-Jul-2014
Date Available: 17-Dec-2021
Language Code: de
DDC Class: 510 Mathematik
MSC 2000: 26-01 Instructional exposition
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 10
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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