The original purpose of this paper was to provide answers to the question: "Why is a negative number time a negative number equal a positive number". This concept is one of the most mysterious topics taught in any mathematics classroom. Yet this fundamental mathematical idea is listed in most algebra text books as a rule without any justification for the validity of the rule. While researching this issue it became clear that the decimal place value system, and in particular the real value

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... system was just as mysterious. Hence the decision was taken to broaden the scope of the paper to include some of the issues associated with the real number system; and to outline some of the topics a mathematics student should be acquainted with.