Completion of the Real Numbers and Its Implications




Wilson, Madison

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The goal of this paper is to explore the completion of the set of real numbers and its overall importance as it pertains to teaching modern mathematics and real-world applications. Cauchy sequences and Dedekind cuts both have advantages and disadvantages when utilized to complete the reals. Both methods help to provide a stronger foundation to the real number system which is very significant to modern mathematics today. Given that the set of real numbers is a complete field, it has a number of implications. It is highly imperative that modern-day students of mathematics have a strong understanding of the properties and axiomatic consequences of this set. By the end of the paper, we hope to develop a clear and thorough comparison of each completion of the real numbers, as well as relate them to real-world applications and education.


Creative Arts and Research Symposium
Creative Arts and Research Symposium