Publication Year

2006

Keywords

Mathematics, Paradoxes, Calculus, Cantor, Halting, Incomplete Theorem, Chaitin's Omega

Disciplines

Mathematics | Physical Sciences and Mathematics

Abstract

I have had the opportunity to reflect on the notions of indeterminacy and incompleteness within various fields associated with mathematics. I initially gained a reading comprehension on paradoxes, emphasizing Russell's paradox of the library. I then studied first order logic, using propositional calculus as a means of examining a formal system which is consistent and complete for the purpose of comparison and future reference. I explored various proofs utilizing the essence of Cantor's diagonal argument, which allowed me the opportunity to better comprehend the ideas of infinity, contradiction, incompleteness, and indeterminacy. All this led to a Halting version proof of Gödel's Incomplete Theorem. I examined the proofs of Gödel's two incompleteness theorems and concluded with a discussion on Chaitin's Omega.

Department 1 Awarding Honors Status

Mathematics

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

Included in

Mathematics Commons

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