An Explicit Mapping of the Real Numbers to the Set of Natural Numbers

By showing that Cantor’s diagonal technique that lists the real numbers does not even work to show the proper cardinality of the rational numbers, we refute his proof technique. To explicitly reference them the real numbers are represented as the limit of partial decimal sums. We show that the real numbers are a denumerable set. We create a new (Level Set Theory), where all infinite sets have the same cardinality as the set of natural numbers.