Abstract: In high school mathematics, and much of college mathematics, the real numbers are taken for granted. This includes non trivial properties (such as the Completeness Axioms) which are also basically just "taken for granted". In this talk we will give the basic outline of Georg Cantor's approach to constructing the real numbers from the rational numbers. This involves the careful consideration of a natural equivalence relation which may be placed on sequences of rational numbers. (Around the same time Dedekind outlined a procedure for constructing the real numbers from the rationals using "cuts". We will not discuss Dedekind's approach in this talk.)