Unification Theorem
Cantor has provided us with an infinite sequence of transfinite cardinals and their powersets. The class of subsets of a cardinal with cardinality the same as the original cardinal, we will call the combinatorial set of the
cardinal. Our two axioms show that the cardinality of the powerset and the combinatorial set are the same.
An aside: a disappointing feature of set theory is that the largest infinite collection, the Absolute Infinity, cannot be made part of set theory. Cantor has shown that, if we attempt to make it a part, contradictions will be the result. Thus, just as there is no largest integer, there is no largest cardinal either. See the frame below.