Enquiry concerning the hyperreal number system.

Abstract

The hyperreal number system has been developed since the 1960s, starting with the ground-breaking work of Abraham Robinson, for the purpose of doing nonstandard analysis [10]. The main motivation for its development derives from the goal to conceptualize historically controversial numbers, namely innitesimals and innities. In this thesis, my goal is first of all to provide a complete but concise construction of the hyperreal number system that functions as the basic conceptual frame of nonstandard analysis, and second of all to investigate some fundamental properties of the system that determines the way in which nonstandard analysis can be conducted. This thesis can be considered as an original synthesis primarily of [5], [4], and [10].