Abstract
In the article 'There are Truth and Beauty in Undergraduate Mathematics Research’, the author posted a problem regarding the closure properties of irrational and transcendental numbers under addition and multiplication. In this study, we investigate the problem using elementary mathematical methods and provide a new approach to the closure properties of irrational numbers. Further, we also study the closure properties of transcendental numbers. KEYWORDS: Irrational numbers; Transcendental numbers; Dedekind cuts; Algebraic numbers
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