Nevertheless, Cantor noticed that if one collects together all the countable ordinal numbers, i.e., the numbers representing well-orderings of the set of natural numbers, this collection, which Cantor called the second number-class (the first being the set of natural numbers), must be of greater cardinality than that of the collection of natural numbers itself. Moreover, this size is the cardinal successor to the size of the natural numbers in the very clear sense that any infinite subset of the second number-class is either of the power of the natural numbers or of the power of the whole class; thus, there can be no size which is strictly intermediate. The process generalises: collect together all the ordinal numbers representing well-orderings of the second number-class to form the third number-class, and this must be the immediate successor in size to that of the second number-class, and so on. In this way, Cantor could use the ordinal numbers to generate an infinite sequence of cardinalities or powers. This sequence was later  (Cantor 1895) called the aleph-sequence, ℵ0 (the size of the natural numbers), ℵ1 (expressing the size of the second number-class), ℵ2 (expressing the size of the third number-class), and so on. Since the intention was that ordinal numbers could be generated arbitrarily far, then so too, it seems, could the alephs.