{"id":{"repo_id":"govst","oai_identifier":"oai:opus.govst.edu:theses-1099"},"canonical_url":"https://search.dev.ndltd.org/etd/govst/oai:opus.govst.edu:theses-1099","repository":{"repo_id":"govst","name":"Governors State University","base_url":"https://opus.govst.edu/do/oai/"},"display":{"title":"Transfinite Ordinal Arithmetic","abstract":"Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion, a table of many simplified results of ordinal arithmetic with these three operations are presented.","abstract_html":"Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion, a table of many simplified results of ordinal arithmetic with these three operations are presented.","abstract_has_math":false,"creators":["Clark, James Roger"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["J. Christopher Tweddle, Ph.D.","Andrius Tamulis, Ph.D.","Jing Zhang, Ph.D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-07-13T07:00:00Z","date_published":"2017-07-13T07:00:00Z","updated_at":"2026-07-24T02:24:36Z","subjects":["Mathematics","Number Theory","Set Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus.govst.edu/theses/97","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["J. 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The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion, a table of many simplified results of ordinal arithmetic with these three operations are presented."]},{"key":"dc:title","label":"Title","values":["Transfinite Ordinal Arithmetic"]}]}],"canonical_facts":{"dc:contributor":["J. Christopher Tweddle, Ph.D.","Andrius Tamulis, Ph.D.","Jing Zhang, Ph.D."],"dc:creator":["Clark, James Roger"],"dc:description.abstract":["Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion, a table of many simplified results of ordinal arithmetic with these three operations are presented."],"dc:identifier":["https://opus.govst.edu/theses/97"],"dc:subject":["Mathematics","Number Theory","Set Theory"],"dc:title":["Transfinite Ordinal Arithmetic"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T02:24:36Z"}