Abstract

Infinitesimal elements are mainly considered in non-standard analysis. Recently a new scale free analysis
has been developed using the concept of relative infinitesimals, scale free infinitesimals and their
corresponding non-archimedean absolute value. With this valuation the real number system R has been
extended to an infinite dimensional non-archimedean system R accommodating infinitely small and large
numbers. In this paper we present a comparison study of non-standard analysis and non-archimedean
ultrametric theory.