 the power set) of the natural numbers, and Cantor's diagonal argument states that the latter set's cardinality is strictly greater than the cardinality of N. Since the set of algebraic numbers is countable, almost all real numbers are transcendental.The non-existence of a subset of the reals with cardinality strictly between that of the integers and the reals is known as the continuum hypothesis.The continuum hypothesis can neither be proved nor be disproved; it is independent from the axioms of set theory.