We say that the natural numbers have infinite cardinality and the real numbers have infinite cardinality , but the cardinality of the real numbers is greater than the cardinality of the natural numbers . The hypothesis states that the set of real numbers has minimal possible cardinality which is greater than the cardinality of the set of integers . Equivalently , as the cardinality of the integers is ( `` aleph-naught '' ) and the cardinality of the real numbers is , the continuum hypothesis says that there is no set for which