Whole numbers have names that describe numbers. The word pi is the name of a set that contains power series to measure the circumference of a circle. It is the name of a set, not a number. This essay describes the nature of rational and irrational numbers in terms of power series. It uses the Axiom of Infinity and the Axiom of Choice. The coefficients of the powers of ten to a minus integer are independent random draws from the integers her to nine. This process enable a clear distinction between rationals and irrationals.