Enquiry concerning the hyperreal number system.
| dc.contributor.author | Wu, Tianyu. | |
| dc.date.accessioned | 2016-03-22T20:17:40Z | |
| dc.date.available | 2016-03-22T20:17:40Z | |
| dc.date.issued | 2015 | |
| dc.description | ii, 58 leaves. | en_US |
| dc.description | Includes bibliography: leaves 57-58. | |
| dc.description.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]. | en_US |
| dc.description.tableofcontents | Tools from first order logic : language and structure -- Language -- Structure -- The construction of the hyperreal number system -- The real number system R -- The hyperreal number system H -- Justifications of the hyperreal number system -- The transfer principle : use/misuse and applicability/non-applicability -- Investigations of some important properties of the hyperreal number system -- Basic categorizations of hyperreals -- Topological properties of hyperreals -- Abstract algebraic properties of hyperreals. | |
| dc.identifier.other | W Thesis 1497 | |
| dc.identifier.uri | http://hdl.handle.net/11040/24328 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Wheaton College (Norton, Mass.) | en_US |
| dc.subject | Undergraduate research. | |
| dc.subject | Undergraduate thesis. | |
| dc.subject.lcsh | Robinson, Abraham, 1918-1974. | |
| dc.subject.lcsh | Nonstandard mathematical analysis. | |
| dc.subject.lcsh | Calculus. | |
| dc.subject.lcsh | First-order logic. | |
| dc.title | Enquiry concerning the hyperreal number system. | en_US |
| dc.type | Thesis | en_US |