{"id":{"repo_id":"texas-state","oai_identifier":"oai:digital.library.txst.edu:10877/21672"},"canonical_url":"https://search.dev.ndltd.org/etd/texas-state/oai:digital.library.txst.edu:10877/21672","repository":{"repo_id":"texas-state","name":"Texas State University","base_url":"https://digital.library.txst.edu/server/oai/request"},"display":{"title":"The Infinite Ladder in Mathematics: Transfinite Induction","abstract":"This project explores the mathematical proof method of transfinite induction. Transfinite induction is mathematical induction beyond the natural numbers. These numbers are called ordinals, denoted by Greek letters. This thesis will introduce fundamental concepts of set theory, starting from the formal definition of natural numbers. We aim to provide a clear development of set theory by building definitions and theorems sequentially with examples and explanations. 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Transfinite induction is mathematical induction beyond the natural numbers. These numbers are called ordinals, denoted by Greek letters. This thesis will introduce fundamental concepts of set theory, starting from the formal definition of natural numbers. We aim to provide a clear development of set theory by building definitions and theorems sequentially with examples and explanations. 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