Preprint 10-2014

Prinzipien einer Standard Analysis

Author(s) : Michael Pfender

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2014

MSC 2000

26-01 Instructional exposition

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.

Keywords : real functions, real numbers, quaternion analysis