A further difficulty is that the lack of the notion of function makes the general theory of the comparison of sets by size (or indeed by order) cumbersome. Zermelo does develop a way of expressing, for disjoint sets a, b, that a is of the same size as b, by first defining a ‘product’ of two disjoint sets, and then isolating a set of unordered pairs (a certain subset of this product) which ‘maps’ one of the sets one-to-one onto the other. But this is insufficiently general, and does not in any case indicate any way to introduce ‘the’ size of a. Russell's method (defining the cardinality of M as the set card(M) = {N : N ∼ M} (where ‘∼’ means ‘cardinally equivalent to’) is clearly inappropriate, since with a set a = {b}, card(a) (which should be the cardinal number 1) is as big as the universe, and the union set of 1 would indeed be the universal ‘set’. Over and above this, there is the more specific problem of defining the aleph numbers.