@MISC{Sng_constructionof, author = {Gary Sng and Chee Hien and Denny Leung Ho-hon}, title = {Construction Of The Real Number System}, year = {} }

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Abstract

Currently, there is no modules in the mathematics department of NUS that offer a rigorous treatment of the construction of the real number system. The real number system is simply taken for granted, with all its associated properties. Although this current approach of assuming the existence of the real number system is unarguably reasonable and practical for most undergraduate mathematics, it does have several drawbacks. Firstly, since the real number system is so fundamental to mathematics, at least at the undergraduate level, the omission of the treatment of its construct on would seem to represent a knowledge gap in the average mathematics studentâ€™s training. Secondly, although most mathematics student may causally dismiss the real number system as intuitively obvious, there is cause for concern that this perspective was borne out of familiarity, and not intuition. For example, can anyone easily visualize an irrational number or give an intuitive argument for its existence? Why is it that the order completeness property holds in the real number system, or, from an axiomatic