The Real Numbers System and Why a Negative Number Times a Negative Number Equals a Positive Number

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 number 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.