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Thesis-Final.pdf (510.79 KB)
ETD Abstract Container
Abstract Header
Internal Set Theory and Euler's Introductio in Analysin Infinitorum
Author Info
Reeder, Patrick F
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1366149288
Abstract Details
Year and Degree
2013, Master of Science, Ohio State University, Mathematics.
Abstract
In Leonhard Euler's seminal work
Introductio in Analysin Infinitorum
(1748), he readily used infinite numbers and infinitesimals in many of his proofs. We aim to reformulate a group of proofs from the
Introductio
using concepts and techniques from Abraham Robinson's celebrated Nonstandard Analysis (NSA); in particular, we will use Internal Set Theory, Edward Nelson's distinctive version of NSA. We will specifically examine Euler's proofs of the Euler formula, the Euler product, the Wallis product and the divergence of the harmonic series. All of these results have been proved in subsequent centuries using epsilontic arguments. In some cases, the epsilontic arguments differ significantly from Euler's original proofs. We will compare and contrast the epsilontic proofs with those we have developed by following Euler more closely through NSA. We claim that NSA possesses the tools to provide appropriate proxies of some--but certainly not all--of the inferential moves found in the
Introductio
.
Committee
Warren Sinnott (Committee Chair)
Stewart Shapiro (Committee Member)
Pages
54 p.
Subject Headings
Logic
;
Mathematics
Keywords
Euler
;
Nonstandard analysis
;
Internal Set Theory
;
Infinitesimal
;
Infinite
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Citations
Reeder, P. F. (2013).
Internal Set Theory and Euler's Introductio in Analysin Infinitorum
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366149288
APA Style (7th edition)
Reeder, Patrick.
Internal Set Theory and Euler's Introductio in Analysin Infinitorum.
2013. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1366149288.
MLA Style (8th edition)
Reeder, Patrick. "Internal Set Theory and Euler's Introductio in Analysin Infinitorum." Master's thesis, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366149288
Chicago Manual of Style (17th edition)
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Document number:
osu1366149288
Download Count:
1,415
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.