{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/44960"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/44960","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Hyperreal structures arising from an infinite base logarithm","abstract":"This paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of \"nonstandard analysis\". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the fundamental results of nonstandard analysis which are used throughout the paper. The new theory which is built upon this foundation organizes the set hyperreal numbers through structures which on an infinite base logarithm. Several new relations are introduced whose properties enable the simplification of calculations involving infinite and infinitesimal The paper explores two areas of application of these results to standard problems in elementary calculus. The first is to the evaluation of limits which assume indeterminate forms. The second is to the determination of convergence of infinite series. Both applications provide methods which greatly reduce the amount of con1putation necessary in many situations.","abstract_html":"This paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of "nonstandard analysis". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the fundamental results of nonstandard analysis which are used throughout the paper. The new theory which is built upon this foundation organizes the set hyperreal numbers through structures which on an infinite base logarithm. Several new relations are introduced whose properties enable the simplification of calculations involving infinite and infinitesimal The paper explores two areas of application of these results to standard problems in elementary calculus. The first is to the evaluation of limits which assume indeterminate forms. The second is to the determination of convergence of infinite series. Both applications provide methods which greatly reduce the amount of con1putation necessary in many situations.","abstract_has_math":false,"creators":["Lengyel, Eric"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1996,"date_issued":"1996-04-11","date_published":"1996-04-11","updated_at":"2026-07-22T22:19:10Z","subjects":["infinitesimals","hyperreal numbers","nonstandard analysis","limits","infinite series"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-10012008-063105"],"render_values":[{"text":"etd-10012008-063105","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/44960","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Lengyel, Eric"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:46:41Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:46:41Z","2008-10-01"]},{"key":"dc:date.issued","label":"Date","values":["1996-04-11"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["infinitesimals","hyperreal numbers","nonstandard analysis","limits","infinite series"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-10012008-063105"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/44960"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of \"nonstandard analysis\". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the fundamental results of nonstandard analysis which are used throughout the paper. The new theory which is built upon this foundation organizes the set hyperreal numbers through structures which on an infinite base logarithm. Several new relations are introduced whose properties enable the simplification of calculations involving infinite and infinitesimal The paper explores two areas of application of these results to standard problems in elementary calculus. The first is to the evaluation of limits which assume indeterminate forms. The second is to the determination of convergence of infinite series. Both applications provide methods which greatly reduce the amount of con1putation necessary in many situations."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Hyperreal structures arising from an infinite base logarithm"]}]}],"canonical_facts":{"dc:contributor.department":["Mathematics"],"dc:creator":["Lengyel, Eric"],"dc:date.accessioned":["2014-03-14T21:46:41Z"],"dc:date.available":["2014-03-14T21:46:41Z","2008-10-01"],"dc:date.issued":["1996-04-11"],"dc:description.abstract":["This paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of \"nonstandard analysis\". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the fundamental results of nonstandard analysis which are used throughout the paper. The new theory which is built upon this foundation organizes the set hyperreal numbers through structures which on an infinite base logarithm. Several new relations are introduced whose properties enable the simplification of calculations involving infinite and infinitesimal The paper explores two areas of application of these results to standard problems in elementary calculus. The first is to the evaluation of limits which assume indeterminate forms. The second is to the determination of convergence of infinite series. Both applications provide methods which greatly reduce the amount of con1putation necessary in many situations."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-10012008-063105"],"dc:identifier.uri":["http://hdl.handle.net/10919/44960"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["infinitesimals","hyperreal numbers","nonstandard analysis","limits","infinite series"],"dc:title":["Hyperreal structures arising from an infinite base logarithm"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:10Z"}